Leading Leave campaigners have claimed it would be “disastrous” if a vote to quit the European Union sparked a Conservative Party leadership contest.
Brexit-supporting Cabinet ministers have insisted David Cameron must remain in Downing Street to lead the negotiations pulling Britain out of the 28-member bloc.
The comments follow a weekend of speculation about the Prime Minister’s future sparked by former chancellor Ken Clarke’s claim that Mr Cameron “wouldn’t last 30 seconds” if he loses the 23 June referendum.
But House of Commons Leader Chris Grayling said replacing Mr Cameron would harm the Leave cause.
“I actively want David Cameron to stay, not only because he is a very good prime minister but because he has got the relationships we need around Europe to build a negotiating process,” he told BBC One’s The Andrew Marr Show.
“It would be disastrous in my view for the Leave cause if we vote to leave and then we get distracted by a leadership contest.”
But senior Tory David Davis told Marr the Prime Minister would have to appoint someone that the party and the public had faith in to lead the negotiations.
“If he did that, I don’t see any reason why he shouldn’t go on,” he added.
Brexit campaigners continued to dismiss interventions from international leaders and organisations about Britain’s future in the EU.
Ahead of the upcoming visit by Barack Obama, Mr Grayling suggested the US president “perhaps doesn’t understand” the shift in power that has taken place between the UK and Brussels.
“I can only think he doesn’t realise,” he said.
Mr Grayling also insisted that claims by French economy minister Emmanuel Macron that his country would end an agreement that effectively moves Britain’s border over the Channel were a “red herring”.
Mr Grayling said: “This is a great red herring. Let’s be clear, the French government, the French interior minister, have said very clearly that won’t change.”
Mr Macron said the EU would have to show there were “consequences” of Brexit in its negotiations with Britain, otherwise “everybody who disagrees on one or two points will decide to do the same”.