David Cameron should stay on as PM to lead negotiations if the UK votes to leave the EU, two cabinet ministers have said.
Commons Leader Chris Grayling, who backs a Leave Vote, told the BBC: "He must stay, I want him to stay."
Northern Ireland Secretary Theresa Villiers told Sky he was the "right man to take us out of the European Union".
It comes after former chancellor Ken Clarke suggested the PM "wouldn't last 30 seconds if he lost the referendum".
Although Mr Cameron is campaigning for the UK to remain in the European Union, many Conservative MPs, and some members of his own cabinet, are campaigning to leave.
Mr Clarke, a veteran pro-European Conservative, told the BBC last week it was "farcical" to suggest Mr Cameron would be able to remain prime minister if the UK votes to leave the EU in the 23 June referendum, despite campaigning to remain in.
He predicted the party would be "plunged into a Conservative leadership crisis".
But Commons leader Mr Grayling told BBC One's Andrew Marr Show: "I actively want David Cameron to stay, not only because he's a very good prime minister, but because he actually has got the relationships we need around Europe to build the negotiating process.
"It would be disastrous, in my view, for the Leave cause if we vote to leave and then we get distracted by a Conservative leadership contest. He must stay, I want him to stay."
He said the PM could be "part of a team" which would negotiate Britain's exit from the EU but added "it needs people who want to leave in that team as well".
David Davis, the former shadow home secretary, told the programme he believed the PM could stay on but would have to appoint someone "who believed in the negotiation" to lead exit talks.
And Northern Ireland Secretary Ms Villiers, who is also backing the Leave campaign, told Sky News: "It's vitally important that he stays regardless of the vote in the referendum because he's a great prime minister".
Mr Cameron himself has said he would stay on as prime minister, even if he ended up on the losing side.
But Suzanne Evans, the former UKIP deputy chairwoman who is on the board of Vote Leave, said Mr Cameron had made a "terrible job" of his EU negotiations ahead of the referendum and she believed he should resign, if the UK votes to leave. She told Pienaar's Politics: "I don't particularly want him to be negotiating on our behalf."
The official referendum campaigning period began on Friday and rows have continued about the potential impact of leaving the EU on trade, the single market and farm funding.
Farming subsidy row
Labour's Yvette Cooper warned it could cost "£100bn worth of trade" and lead to a loss of manufacturing jobs adding: "It's working class people across Britain who will be hardest hit if we end up losing those jobs".
And French economy minister Emmanuel Macron said the EU would have to show there were "consequences", if Britain left the bloc "otherwise that is the beginning of the dismantling" of the union. Those consequences would include "access to the single market, because you will be no more part of the club," he said.
But Mr Grayling said it was not realistic to suggest European leaders would want to jeopardise trade with the UK because "there are millions of European jobs that depend on British consumers": "We buy far more from the European Union than they buy from us."
Meanwhile, ahead of a National Farmers Union meeting, the UK's Commissioner to the EU Lord Hill said he believed leaving the bloc would bring "more barriers and would be likely to lead to a system where there are cuts in support" for British farmers - particularly as the UK Treasury continued to look for savings.
But pro-Leave farming minister George Eustice said it was not up to the Treasury but Parliament, which would be able to "assert itself" if it took back control of farming policy.
England cricket legend Ian Botham has added his voice to the Leave campaign. Describing the European Union as "racket" in a piece for the Sunday Times he said it was "insane" that Britain was restricted in its trade with "natural friends" outside the EU.
Meanwhile US President Barack Obama is expected to repeat his support for Britain's EU membership when he visits the UK next week.
Liam Fox, the Conservative former defence secretary who is backing the Leave campaign, told BBC One's Sunday Politics: "Of course the American president is there to express what he believes is in America's interest, not Britain's interest... It's absolutely unthinkable that the United States would allow a court to overrule the Supreme Court or someone else to determine their external borders."
But former US State Department spokesman James Rubin responded: "America is a very, very large country. It's a superpower... Just because we won't do something, doesn't mean that the British shouldn't."