Boris Johnson has attacked the government's pledge to cut net migration, saying ministers know it is "legally impossible" to achieve.
The ex-London mayor said EU membership made it impossible to control immigration and criticised politicians who "promise that they can control it".
Remain campaigners pointed to his previous pro-migration comments.
Mr Johnson also said he did not regret his comments about Barack Obama's "part-Kenyan" ancestry.
He had faced criticism after suggesting the US president had an "ancestral dislike of the British Empire" after he spoke out in favour of the UK remaining in the EU.
Speaking as he launched a Vote Leave battle bus to campaign ahead of the 23 June referendum, he said "of course" he did not regret the comment because Mr Obama's intervention had been "absolutely absurd".
Mr Johnson is one of the most high-profile figures in the Leave campaign and among the favourites to replace David Cameron as Conservative leader.
Speaking on BBC Radio 4's Today programme, he focused his criticism on the government's flagship pledge to reduce annual net migration to the tens of thousands.
Ministers admit their efforts have been "blown off course" by EU migration, but it remained an "ambition" in the 2015 general election manifesto.
Home Secretary Theresa May recently admitted the founding principle of free movement within the EU makes it more difficult to curb immigration to the UK.
Mr Johnson said immigration could be a good thing and that London had benefited from "an influx of talented people".
But he said the government had "absolutely no control" over the numbers coming from the EU, adding: "What's certainly not a good idea, politically, is for politicians to stand up year after year and tell the British people 'we can cut immigration to tens of thousands' when they know full well that that's legally impossible."
He added: "Uncontrolled immigration is politically very damaging, particularly when politicians promise that they can control it."
It causes "huge unfunded pressures" for the NHS and public services, he added.
The Stronger In campaign said: "In 2014, Boris said 'the country benefits massively from immigration'.
"What has changed his view in two years?"
Former prime minister Gordon Brown, meanwhile, has entered the debate on the Remain side.
Mr Brown said it was "not British to retreat to Europe's sidelines", arguing Britain needed to be in the EU to shape the continent's responses to terrorism, immigration and climate change.
- Subscribe to the BBC News EU referendum email newsletter and get a weekly round-up of news, features and analysis on the campaign sent straight to your inbox.