Crispin Blunt says he is putting the party first
Tory leader Iain Duncan Smith has dismissed the resignation of one of his frontbench team as "irrelevant".
Crispin Blunt says he quit as a trade and industry spokesman as polls closed for Thursday's elections in order to trigger a leadership election.
But Mr Duncan Smith, speaking after the Tories' successful night at the polls, said members of his party were "sick to the back teeth" of talk of plots against the leadership.
He said: "It is about time that we looked at the people who do this and say they are irrelevant because they do not represent the party."
He said the British people were not interested "in who did what to whom in the Conservative Party".
"Crispin Blunt is somebody that nobody has ever heard of outside of
the process," said the Tory leader.
"He's made his position clear, he's disgruntled, you get that in all
"Political parties have divisions where people disagree but we shouldn't
centre on one junior member of the front bench."
Mr Blunt said on Friday that Mr Duncan Smith was "not making the necessary impact" to be judged a credible future prime minister.
He was speaking after the Conservatives celebrated gains of more than 540 council seats in England and Scotland.
Mr Blunt claimed he was not a "stalking horse" for potential leadership contenders, but warned there were at least "five or six candidates" who could challenge Mr Duncan Smith.
But Conservative chairman Theresa May said party members will "feel let down by him" and wonder "what on earth he is doing".
"Frankly, he looks just a little silly now for having done this before he waited to see what the results were like," she told the BBC.
Mr Blunt said he made his decision after failing to persuade the Tory leader to step down or at least put himself to a vote of confidence among party members.
"I resigned after the polls closed, or it became public after the polls closed, so it would have absolutely no impact on the 8,000 or so Conservative candidates and their campaigns up and down the country," he told BBC Radio 4's Today programme.
While securing 35% of the vote was a "very satisfactory state of affairs" for Tory councillors, it was not nearly enough "for putting us on a path to becoming the next government", he said.
"Frankly, everyone knows that Iain Duncan Smith is not making the impact we would all like him to be as our leader and is not making the necessary impact to carry credibility with the electorate as the alternative prime minister," said the Reigate MP.
The party had to decide whether to "carry that handicap" to a general election "whatever the individual merits" of Mr Duncan Smith.
No 'stalking horse'
But Mr Blunt insisted he was "not associated with any of the other potential alternatives" to the Tory leader.
Mr Blunt said while he did not think former leader William Hague was ready for a come back "yet", he did have a potential career of 30 years front line politics ahead of him and would "at some stage in that time ... be prime minister".
The MP admitted trying to trigger a leadership election.
"I have taken this action in order to try and make that happen because I believe that it is in the best interests of the whole Conservative party.
"I know there are thousands of Conservative supporters up and down the country who are saying 'thank God someone is saying this in public - thank goodness the issue may now be addressed'."
Tony Collinson, chairman of Mr Blunt's constituency association, said the MP had been thinking about resigning from the front bench "for a very long time".
"I believe that he felt that this was the right time to do it and I support him wholeheartedly," he told BBC Radio 4's Today programme.
Mr Collinson said he did not think Mr Duncan Smith was leading the party where it ought to be moving and suggested Mr Hague would make a better alternative.
John Reid, Labour's Leader of the Commons, said he was "as bemused as the rest of the nation" about Mr Blunt's departure.
"It really is extraordinary that the Conservative Party could have inflicted such a disaster on itself before the first vote has even been counted," Dr Reid told BBC News 24.
Liberal Democrat Chairman Mark Oaten had a similar message.
He said: "Crispin Blunt's disaffection with the Conservative Party leader is
"However, changing leaders will not change the fortunes of the Conservatives."