Staging a coup against David Cameron in the wake of the local elections results would be 'bonkeroony", according to Michael Gove.
The education secretary said he had "no respect" for Tory MPs, councillors or party members who thought it would be a good idea to hold a leadership election.
Thursday's local elections saw a surge in support for Ukip, with Nigel Farage's party hurting the Tories from the right.
One local councillor who lost their seat told the Daily Telegraph they did not "believe a word" Cameron said. Another told BBC Radio 4's World at One that the prime minister had been given "long enough" and lacked the "strong leadership" needed.
Gove told the BBC said it was "barmy" to call for Cameron's head. "Of course we shouldn't have a leadership election," he said. "The idea of changing the leader is bonkeroony."
Arguing that divided parties do not win elections, Gove added: "Any of my colleagues who want to indulge in leadership speculation should spend the weekend reading the history books."
Farage has hailed today's election results as "remarkable" and said it would send "shockwaves" through Westminster and the British political system.
However Gove said when it came to the general election in 2015 many Ukip voters would return to the fold and vote Tory in order to keep Ed Miliband out of Downing Street.
"Those people who are voting for Ukip are emphatically not people who are likely to vote for Miliband," he said. "Many of those who have voted for Ukip will support the Conservatives."
Embarrassingly for the prime minister the Labour party managed to snatch the Witney South and Central council seat in Cameron's Oxfordshire constituency - with the Tory candidate falling to third place behind Ukip.