Conservative MPs Nicholas Soames and Tim Yeo have quit the shadow cabinet saying they want to be free to play a role in rethinking the party's future.
Mr Howard met new Tory MPs at Westminster
The resignations came as 54 new Tory MPs were welcomed by party leader Michael Howard at the House of Commons.
Mr Yeo wants the focus on climate change but has refused to rule himself out of a bid for the Tory leadership.
Mr Soames says Europe and planning are also important, but says suggestions he wants the leadership are "stupid".
The resignations follow Mr Howard's announcement on Friday that he is to step down once the party's leadership election rules are changed.
Mr Soames said he was keen to join the executive of the Conservatives' backbench 1922 committee.
But he rejected speculation that he would challenge Sir Michael Spicer as the committee's chairman, saying he would rather have "root canal surgery without a bloody anaesthetic".
When it was suggested his resignation might be interpreted as the start of a leadership campaign, Mr Soames said: "Don't be so bloody stupid."
Mr Yeo side-stepped a similar question on BBC Radio 4's Today programme, saying he intended to set out the agenda he thinks the party and its leader should address.
"It's perfectly possible my colleagues will think I'm talking complete nonsense, in which case, I certainly won't be a candidate," he said.
Mr Yeo said it would have been wrong to speak out from the frontbenches because Mr Howard ran a disciplined shadow cabinet.
While the Tories had done well on core issues like crime, taxation, immigration and choice in public services, the party needed to widen its appeal.
Mr Yeo said he wanted to boost the share of the Tory vote from 33-40% by talking about issues like the environment, which had served the Lib Dems well, and protection of the countryside and work/life balance.
"I really do believe that there is a huge section of younger voters, of AB voters, where alarmingly our share of the vote is going down each election."
Mr Yeo said redefining the Conservative agenda over the next four years would be "the first and essential step towards getting back into government".
Meanwhile, Tory deputy leader Michael Ancram refused to comment on speculation that he is also ready to leave.
Tory frontbencher John Redwood also remained tight-lipped about his own leadership ambitions.
Soames says he wants to get on with life on the backbenches
"By all means talk to me when we have a leadership election up and running or in prospect. That is not the current position."
Mr Redwood said he wanted to be part of a general debate about how to improve politics.
He also appeared to criticise his party's campaign, which he said concentrated on immigration, at the cost of debate on the environment, world poverty and the planet.
Theresa May, shadow secretary of state for the family, said the party had to consider its impact at the general election before debating its future direction and leadership.
Welcoming his party's new MPs to Parliament on Monday, Mr Howard said: "I am absolutely convinced that this splendid intake, brimming with talent, is going to set the scene for the next Conservative victory".