Cunliffe, 49, was Labor's Minister of Health and Minister for Communications and Information Technology from October 2007 to November 2008.
After Labor's defeat by the National Party in November 2008, and the resignation of Helen Clark as party leader, Cunliffe was appointed the party's finance spokesman.
Following the 2011 Labor loss, Phil Goff stood down as party leader and Cunliffe ran for the leadership but lost to David Shearer.
It was Shearer's surprise resignation last week -- after less than two years as leader -- that sparked the leadership contest.
Fairfax Media reported Cunliffe saying he was "optimistic" he had Clark's backing.
He also was bullish about Labor's prospects of unseating National Party Prime Minister John Key in a general election expected in November 2014.
"Book a very long holiday in Hawaii, John," Cunliffe said.
"I'm deeply saddened this government is so intent on cutting deals for its big business mates and kowtowing to powerful foreign interests, that it is willing to sacrifice so much of what we hold dear."
Cunliffe is up against deputy Labor leader Grant Robertson, 42, and former minister Shane Jones, 53.
A TVNZ-Colmar Brunton poll Aug. 25 indicated 29 percent of respondents supported Cunliffe ahead of rivals Robertson at 10 percent and Jones at 11 percent.
The center-right National Party formed a minority government after being re-elected in 2011.
Key governs in the 121-seat Parliament with the agreed backing of ACT New Zealand, the United Future Party and the Maori Party for a seven-seat majority.
Shearer, in his resignation statement, said there "was no letter, no ultimatum, no vote" that forced his hand.
"But from the soundings I have taken from colleagues I realize I no longer enjoy the confidence of a number of my caucus colleagues."
Shearer was elected to Parliament in 2009. He worked overseas for the United Nations and was named New Zealander of the Year by the New Zealand Herald in 1993 for his work in Somalia.
"After spending the last 20 years of my life leading humanitarian and reconstruction projects overseas, I came home to New Zealand because I'm passionate about this country," he said.
"The ambitions of one person should never be larger than that greater purpose," Shearer said.
"It's time for someone else to take up the challenge of leader."
But Key, 52, told TVNZ's Breakfast program this week Shearer jumped before he was pushed.
"Obviously they were about to knife him this week, basically, so he just had no option but to quit prior to that," he said.
"David's a good guy, a decent guy actually, leading a really divided caucus. And they are really divided.
"We're going to have now three weeks of what can only be described as reality TV where they'll go out there talking about how much they are the best candidate -- basically code for 'We don't like the other person,'" Key said.