In a speech in central London, the Shadow Education Secretary delivered a damning verdict on Mr Miliband's strategy, saying the party under him "lacked political courage".
Mr Hunt said he had decided against standing because he feared it would have split the centrist vote in the party and could even have deprived the party of a third candidate to take on front-runners Andy Burnham and Yvette Cooper.
Candidates need to be nominated by at least 35 Labour MPs to enter the race and Mr Hunt admitted he had struggled to find a sufficient number of colleagues to back him.
“This morning I am announcing that I will not be entering the race to be leader of the Labour party," he told an audience at the Demos think tank. "Over the last few days I have made a lot of calls to potential supporters. I found that the bulk of MPs are already committed to just a couple of candidates.
"It is clear to me that I do not have sufficient support to be certain that I can run for the leadership myself. Instead today I am offering my endorsement to my colleague Liz Kendall.”
Mr Hunt's decision not to stand leaves four candidates in the contest. Mr Burnham is the front-runner, along with Ms Cooper, Ms Kendall and Mary Creagh.
It now leaves Ms Kendall as the leading modernising candidate, but there are fears she will struggle to win the necessary 35 nominations.
Who will be the next Labour leader?
Who will be the next Labour leader?
1/7 Andy Burnham
Andy Burnham has promised to restore the party's "emotional connection with millions of people," if elected
2/7 Mary Creagh
Mary Creagh has called on her party to win back “Middle England”
3/7 Liz Kendall
Shadow health minister Liz Kendall is seen as a Blairite
4/7 Yvette Cooper
Shadow home secretary Yvette Cooper became the fourth person to join the Labour leadership race
5/7 Tristram Hunt
Tristram Hunt, the shadow Education Secretary, has said he will not run for the Labour leadership as he had not gathered the required nominations of 35 MPs. He has instead endorsed the moderniser Liz Kendall.
6/7 Dan Jarvis
One of the favourites to succeed Ed Miliband as Labour leader – ex-Army paratrooper Dan Jarvis – has ruled himself out, saying he won't do it because of his children
7/7 Chuka Umunna
Chuka Umunna dropped out of the Labour leadership contest just three days after he announced he was in the running
In a lengthy speech on the future direction of the Labour party, Mr Hunt urged the leadership candidates to offer an "inclusive Labour project" that appeals to its lost supporters in Scotland, traditional voters in Labour communities and swing voters tempted by the Conservatives in marginal seats.
Labour needs "a marriage between new Labour’s desire to back wealth creators with Ed Miliband’s urgency to tackle inequality," he said. "A new political landscape of family, community, work and national identity at its heart."
Admitting that Labour had been a divided party over the last five years, he said this had allowed the Tories to take the initiative on issues such as devolution.
"Ed Miliband had a big devolution agenda," he said. "He understood that handing power back is not just about local decision-making and democracy but about meeting the great challenges of our time. Rebalancing the economy; raising productivity; tackling inequality; but the truth is that collectively we dithered.
"The Shadow Cabinet was not united. And when they devolved extra powers to a Labour council in Greater Manchester the Tories effectively stole our clothes.
"Now, the Northern Powerhouse did not exactly translate to a corresponding Northern breakthrough. But it sure as hell helped them hold the line. So we must not let the Tories steal this agenda."
The new leader and deputy leader will be announced on September 12 at a special conference, two weeks before the party’s autumn conference in Brighton.
Each of the candidates must secure the backing of at least 35 Labour MPs by June 15 to be able to stand in the leadership election.Reuse content