The pledge, given to a pressure group by Jack Straw, the party's spokesman on home affairs, was accompanied by another commitment to lift the requirement on employers to carry out checks for illegal immigrants among their workers.
This immediately drew the accusation from the Tories that Labour was seeking the "bulk purchase" of ethnic minority votes at the general election.
Tim Kirkhope, Home Office minister responsible for immigration, said last night: "It is another cynical attempt to try to wrap up the ethnic minorities for the Labour vote. I find that distasteful."
He added: "In a sense, it is the bulk purchase of the ethnic vote. It is patronising and cynical in the extreme."
Mr Straw's commitments are contained in a pamphlet being distributed in marginal constituencies by the Confederation of Indian Organisations (UK), representing hundreds of thousands of Asians. The pamphlet will carry quotations from all three main parties about their immigration policies.
Although they say they are politically independent, the organisers believe the pamphlet will encourage Asians to vote Labour.
It quotes from a letter last month from Mr Straw: "The Government's primary purpose rule is unfair and unnecessary. Labour will not operate it. It congests the system and puts couples in the unfair position of having to prove a negative. Under regulations a German citizen can bring a German spouse to the UK whilst a UK citizen may not be able to bring a non-EU spouse into the UK.
"Immigration rules introduced by Labour in the 1970s already require couples to show that a marriage is genuine and will not be a financial burden on the taxpayer if a spouse is entering the UK from outside the EU."
Mr Straw's statement is the latest attempt by the parties to woo the Asian vote. John Major spent part of the Christmas recess visiting the Indian sub-continent which was seen as a signal to Asian voters. He has also recently guaranteed citizenship to around 5,000 stateless Asians in Hong Kong.
Labour's leadership also has been active in building relationships with Asian voters, and Asian businessmen. A poll last week suggested that 70 per cent would vote Labour, a finding that the Tories dispute.
Tara Mukherjee, president of the Confederation, said: "We are politically non-aligned but we think the commitments given by Mr Straw are very important. We cannot marry whom we like. We cannot bring in our children or our parents as of right.
"If my own son wishes to marry a girl in Calcutta, he has to convince the immigration authorities that it is a genuine marriage. What kind of human rights is that?"Reuse content