The Labour MP said the Leave campaign wanted to adopt a "more liberal" approach to migration from outside the EU, therefore potentially worsening the situation - and added that an Australian-style points-based system had not slowed migration to that country.
Ms Cox likewise pointed out that EU migrants "have contributed £20 billion more to our economy than they've taken out in benefits" and that this money should be better directed to education and health services.
And she noted that the free movement of people would only come to an end by leaving the Single Market - a move that she said would have disastrous economic consequences.
She wrote: "We cannot allow voters to fall for the spin that a vote to leave is the only way to deal with concerns about immigration.
"We can do far more to address both the level and impact of immigration while remaining in the EU. I very rarely agree with the Prime Minister but on this he’s right: we are stronger, safer and better off in."
Both sides of the EU debate suspended their campaigns following the brutal attack on Ms Cox as she left a constituency meeting in Batley and Spen in West Yorkshire, and there has been a national outpouring of condolences and condemnation over her loss.
The suspect charged with her murder, Thomas Mair, gave his name as "death to traitors, freedom for Britain" during his appearance at Westminster magistrates court and evidence has been presented of his links to far-right, white supremacist groups.
Since her death, more than £600,000 has been raised for Ms Cox on a GoFundMe page which has been the biggest and fastest growing fundraising campaign of this kind ever.
Her husband, Brendan, has said his wife would want the UK to "unite to fight against the hatred that killed her."
Mr Cox has also warned that mainstream politicians are "clueless" about dealing with the debate surrounding migration.
"Petrified by the rise of the populists, they try to neuter them by taking their ground and aping their rhetoric," he wrote.
"Far from closing down the debates, these steps legitimise their views, reinforce their frames and pull the debate further to the extremes".
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