Two Labour backbenchers have called for David Miliband to be sacked over an article which led to speculation he wanted to succeed Gordon Brown.
The foreign secretary had "overstepped the line", Geraldine Smith said, while fellow MP Bob Marshall-Andrews accused him of "duplicitous" behaviour.
The Guardian article discussed Labour's future without mentioning Mr Brown.
But Mr Miliband told BBC Radio 2's Jeremy Vine show that he was "not running a leadership campaign".
He insisted Labour was "not down and out", despite last week's by-election defeat in Glasgow East and poor poll ratings.
If David Miliband was placed back on the backbenches, then I think he'd become the non-entity that he was before his accelerated promotion
Geraldine Smith Labour MP
The party was "determined" to be clear about its values, and ensure a "real choice at the next election", he added.
But Ms Smith, the MP for Morecambe and Lunesdale, said Mr Miliband had been "trying to stir up trouble".
"What has David Miliband ever achieved, apart from furthering his own career?" she asked on BBC Radio 4's The World at One.
"If David Miliband was placed back on the backbenches, then I think he'd become the non-entity that he was before his accelerated promotion," she added.
Mr Marshall-Andrews, MP for Medway, accused Mr Miliband of "pretty contemptible politics" in his article.
"The complete and conspicuous absence of mention of the prime minister at this particular stage obviously conveys its own message.
I think it's right that we say that, sure we've taken some hits, but actually we've got ideas about the future of the country
David Miliband Foreign secretary
"It is a quite deliberate message but, as I say, it is a duplicitous message which is the worst possible kind of politics."
He went on: "I think [Mr Brown] should sack him if he doesn't resign and mount a proper leadership challenge."
But the foreign secretary insisted the article had been intended as a challenge to Conservative leader David Cameron rather than to the prime minister.
He said the worst thing for his party would be "if we all went mute" at present.
"I think it's right that we say that, sure we've taken some hits, but actually we've got ideas about the future of the country. We do want to engage with people," Mr Miliband said.
Asked if he wanted to become prime minister one day, he replied: "I always say, 'Focus on the job you've got.'
"Do the day job well. If you worry about your next job, you're not going to do the current job [properly]."
However, BBC political editor Nick Robinson said: "This is a man testing the waters for a leadership bid and a man simply unprepared to come to the defence of a beleaguered prime minister."
Many of Thursday's newspapers claimed Mr Brown's allies were angry at Mr Miliband for perceived disloyalty, although these reports were attributed to unidentified sources within Labour.
But Mr Miliband insisted he always took anonymous quotes "with a very large dose of salt".
Ex-minister Denis MacShane called for an end to such off-the-record briefings against the foreign secretary, saying these risked harming Britain's standing in the world.
Mr Miliband signed and altered a Daily Telegraph headline after his interview
"The national interest is now being damaged by these anonymous attacks on Miliband and they should stop now," he said.
After being played Ms Smith's remarks, Mr Miliband said he "respected" her because she had "put her name" to her comments, rather than staying anonymous.
He replied it was important that senior Labour figures "stand up for ourselves" to counter criticism that their party was not fit to govern.
On Tuesday, Labour's deputy leader, Harriet Harman, insisted she was "not preparing the ground for a leadership election" and said she did not accept Mr Brown's spell as leader was "over".
Health minister Ivan Lewis said Labour must avoid being too "timid" if it wanted to win the next election.
He called on Mr Brown to be a "decisive" leader, saying that "the only way forward now is bold Labour".
Mr Lewis said the measure of any political party was revealed "in the bad time and not the good time".
"We now face the ultimate test. People have a decision to make. But there's one thing that's absolutely clear - it's that the public don't vote for divided parties."
And Mr Lewis added that his party's defeat in Glasgow East, where the Scottish National Party overturned Labour's majority of 13,507, "confirmed my view that timidity and incremental change will not deal with the way people feel right now".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.