Leaving the EU would give the UK an "illusion of sovereignty" but not full control, PM David Cameron has said.
The UK would be "stronger and safer" in the EU and needed to be a member to influence decisions, he told the BBC.
Earlier, UKIP leader Nigel Farage had said a vote to leave would mean the UK was "in charge of our own country".
The PM's pitch came as Tory London mayoral candidate Zac Goldsmith said he would campaign for exit - with Boris Johnson also expected to vote to leave.
BBC assistant political editor Norman Smith said London mayor Mr Johnson had been genuinely conflicted but had now made up his mind - and was expected to announce he was joining the leave campaign.
Mr Cameron's latest comments came as ministers began campaigning to win over voters ahead of a referendum on 23 June over the UK's EU membership.
The prime minister warned that exiting the EU would not stop migrants coming to the UK, as six ministers who attend cabinet joined the leave campaign.
Downing Street has been resigned to Mr Johnson campaigning to leave following a meeting this week which left him disappointed with Mr Cameron's plans on the EU, says BBC political editor Laura Kuenssberg.
Mr Johnson has also discussed the issue with Justice Secretary Michael Gove, one of those to declare support for the leave campaign.
The prime minister announced the date of the in/out referendum outside Number 10 on Saturday, having returned from Brussels with a deal he argued gave Britain a "special status" within the EU.
He warned leaving the EU would be a "leap in the dark" as he urged voters to back his reform deal.
Renegotiations of the UK's relationship with Europe were finalised on Friday night after intense wrangling at a two-day summit in Brussels.
The agreement, which will take effect immediately if the UK votes to remain in the EU, includes changes to allow curbs on migrant welfare payments, safeguards for Britain's financial services and making it easier to block unwanted EU regulations.
The prime minister told the Sunday Times leaving the EU would not stem the flow of migrants coming into the UK.
He said the UK would still have to contribute financially to the EU, even if it left.
He also challenged Eurosceptics to explain what Britain's relationship with Europe would be like in the event of an EU exit.
'Mired in the past'
Meanwhile, splits in the cabinet over the issue have been laid bare by interviews and articles in Sunday's newspapers.
Writing in the Observer, Foreign Secretary Phillip Hammond said "leaving the EU would be a threat to our economic security and our national security".
In an article for the Mail on Sunday, Business Secretary Sajid Javid said he would be voting for the UK to remain in the EU with a "heavy heart" and no "enthusiasm". He said leaving the EU could add to "economic turbulence".
However, Mr Gove - a close friend and key ally of Mr Cameron - wrote in the Sunday Telegraph that the EU was "mired in the past".
He said choosing to join the leave campaign had been "the most difficult decision of my political life".
Northern Ireland Secretary Theresa Villiers told the BBC leaving the EU was a safer option than staying in it.
She said there had been a sense of history at the cabinet meeting to discuss the vote - the first to be called on a Saturday since the Falklands War.
The Labour Party, the SNP, Plaid Cymru and the Lib Dems have said they are in favour of staying in Europe. The DUP said it will recommend voting to leave the EU.
Two campaign groups - Vote Leave and Leave.EU - are competing to be officially designated as the Out campaign for the referendum.
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