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Shadow Chancellor John McDonnell has said migrants are not "to blame for low pay and insecurity" at work.
Mr McDonnell used a keynote speech to hit back against what he called the "cynical" policies of the Conservatives on immigration.
It comes after Theresa May's Tories launched proposals for a wide-ranging new crackdown on immigration at their party conference in Birmingham.
But Mr McDonnell's move may strain underlying tensions over immigration with other key Labour figures, including shadow Brexit secretary Sir Kier Starmer who has said numbers coming into the country should fall.
Mr McDonnell said: "Labour are not about to make cynical promises like the Conservatives on reducing migrant numbers, knowing full well they can't be met on the scale, or time scale, with the methods they propose.
"It is not migrants to blame for low pay and insecurity at work, or the high cost of housing, it is the failure of our whole economic model, which is not supplying the investment in work, or in housing, that people need. We have to change the model."
John McDonnell promises living wage under next Labour government Addressing concerns raised in the EU referendum about migration levels, the shadow chancellor said: "Labour's policy has always been about managed migration, about what the economy needs and what society needs overall.
"What we experienced during the referendum...people voted on a whole range of issues, one of which was their concern about the low standard of living. They actually looked at migration being exploited by employers and others to undermine that standard of living.
"What we will negotiate is a future with Europe that protects people's standards of living, that doesn't allow migration to be used and exploited in that way. And in that way I believe we can build a coherent, cohesive Britain in the future."
Show all 26 Brexit Concerns Brexit will put British patients at 'back of the queue' for new drugs Brexit will put British patients at the “back of the queue” for vital new drugs, the Government has been warned – forcing them to wait up to two years longer A medicines regulator has raised the alarm over a likely decision to pull out of the European Medicines Agency (EMA), as well as the EU itself. ealth Secretary Jeremy Hunt dropped the bombshell , when he said he expected the UK would quit the EMA – because it is subject to rulings by the European Court of Justice.
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Brexit Concerns London to lose status as 'gateway to Europe' for banks One of Germany’s top banking regulators has warned that London could lose its status as “gateway to Europe” for the banking sector after Britain quits the European trading bloc. Andreas Dombret, who is an executive board member for the Bundesbank—Germany’s central bank—told a private meeting of German businesses and banks earlier this week in Frankfurt that even if banking rules were “equivalent” between the UK and the rest of the EU, that was still “miles away from [Britain having] access to the single market”, the BBC reports.
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The number of financial sector professionals in Britain and continental Europe looking for jobs in Ireland rocketed in the months after the UK voted to leave the European Union
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Brexit Concerns Brexit is making FTSE 100 executives richer Pay packages of many FTSE 100 chief executive officers are partly tied to how well share prices are doing rather than the CEO’s performance -- and some stocks are soaring. ritish equities got a boost since the June vote because the likes of Rio Tinto, Smiths Group and WPP generate most sales abroad and earn a fortune when they convert these revenues back into the weakened pound. Sterling’s fall also made UK stocks more affordable for overseas investors.
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Brexit Concerns Theresa May: UK to leave single market Theresa May has said the UK "cannot possibly" remain within the European single market, as staying in it would mean "not leaving the EU at all".
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Lead campaigner Gina Miller and her team outside the High Court
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Raymond McCord holds up his newly issued Irish passport alongside his British passport outside the High Court in Belfast following a judges dismissal of the UK's first legal challenges to Brexit
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SDLP leader Colum Eastwood leaving the High Court in Belfast following a judges dismissal of the UK's first legal challenges to Brexit
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Migrants with luggage walk past a graffiti on a wall as they leave the 'Jungle' migrant camp, as part of a major three-day operation planned to clear the camp in Calais
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Migrants leave messages on their tents in the Jungle migrant camp
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The Adventist Development and Relief Agency (Adra) which distributes approximately 700 meals daily in the northern Paris camp states that it is noticing a spike in new migrant arrivals this week, potentially linked the the Calais 'jungle' camp closure - with around 1000 meals distributed today
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Migrant workers pick apples at Stocks Farm in Suckley, Britain
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Many farmers across the country are voicing concerns that Brexit could be a dangerous step into the unknown for the farming industry
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Bank of England governor Mark Carney who said the long-term outlook for the UK economy is positive, but growth was slowing in the wake of the Brexit vote
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The Dow Jones industrial average closed down over 600 points on the news with markets around the globe pluninging
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Immigration officers deal with each member of the public seeking entry into the United Kingdom but on average, 10 a day are refused entry at this London airport and between 2008 and 2009, 33,100 people were detained at the airport for mainly passport irregularities
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A number of global investment giants have threatened to move their European operations out of London if Brexit proves to have a negative impact on their businesses
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Following the possibility of a Brexit the UK would be released from its renewable energy targets under the EU Renewable Energy Directive and from EU state aid restrictions, potentially giving the government more freedom both in the design and phasing out of renewable energy support regimes
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A woman looking at a chart showing the drop in the pound (Sterling) against the US Dollar in London after Britain voted to leave the EU
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Young protesters outside the Houses of Parliament in Westminster, to protest against the United Kingdom's decision to leave the EU following the referendum
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Applications from Northern Ireland citizens for Irish Passports has soared to a record high after the UK Voted in favour of Leaving the EU
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NFU Vice President Minette Batters with Secretary of State, Andrea Leadsome at the National Farmers Union (NFU) took machinery, produce, farmers and staff to Westminster to encourage Members of Parliament to back British farming, post Brexit
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The latest reports released by the UK Cabinet Office warn that expats would lose a range of specific rights to live, to work and to access pensions, healthcare and public services. The same reports added that UK citizens abroad would not be able to assume that these rights will be guaranteed in the future
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A British resident living in Spain asks questions during an informative Brexit talk by the "Brexpats in Spain" group, about Spanish legal issues to become Spanish citizens, at the town hall in Benalmadena, Spain
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The collapse of Great Britain appears to have been greatly exaggerated given the late summer crowds visiting city museums, hotels, and other important tourist attractions
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The U.K. should maintain European Union regulations covering everything from working hours to chemicals until after the government sets out its plans for Brexit, said British manufacturers anxious to avoid a policy vacuum and safeguard access to their biggest export market
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His tone mirrored that of Jeremy Corbyn, whose spokesman at party conference said he would be "relaxed" if migrant numbers rise .
But Shadow Brexit secretary Sir Keir Starmer said earlier this month there had been a "huge amount of immigration over the last 10 years and people are understandably concerned".
He added: "I think it should be reduced and it should be reduced by making sure we have got the skills in this country that are needed for the jobs that are needed to be done."
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