Angela Eagle has said she can provide the leadership "in dark times for Labour" that Jeremy Corbyn cannot, as she launched her leadership challenge.
Ex-shadow business secretary Ms Eagle said she wanted to bring the party and the country "back together".
Labour Party general secretary Iain McNicol said he had received enough nominations to trigger a contest.
Mr Corbyn has refused to step down since losing the support of most of his MPs in a vote of no confidence.
Launching her leadership bid, Ms Eagle said: "I'm not a Blairite. I'm not a Brownite. I'm not a Corbynista. I am my own woman."
The party's ruling committee, the National Executive Committee, is expected to decide this week whether Mr Corbyn needs the backing of MPs to stand in the contest.
'Divided and uncertain'
Ms Eagle said she would not have stood for leader "if I did not think I could be a good prime minister for Britain".
"These are dark times for Labour. And they are dangerous times for our country."
Ms Eagle said Mr Corbyn, who has faced numerous frontbench resignations - including her own on 27 June - was unable to hold the government to account and then replace it by winning a general election.
"Jeremy Corbyn is unable to provide the leadership this huge task needs," she said.
"I believe I can."
When asked if her chances were doomed if Mr Corbyn was allowed on the leadership ballot paper, she said: "I don't go in for suicide missions."
She said the EU referendum result had left the UK "divided and uncertain".
While she had supported the Remain campaign, she said the vote to leave was for many "a howl of pain".
The questions now were how to bring hope to parts of the country that felt neglected, how to protect jobs, investment and living standards and how to remain an open, tolerant society, she said.
Ms Eagle said she would "not stand back and allow Britain to become a one-party Tory state".
"It's about giving hope to people all over the country that Labour can be an alternative government, ready and equipped to serve," she said.
"I will unite, I will not divide. I can bring our party together again."
Profile: Angela Eagle
- First elected as MP for Wallasey in 1992, Ms Eagle was one of the youngest MPs in Parliament at age 31
- The Yorkshire-born MP was comprehensive school-educated before going to Oxford University to read philosophy, politics and economics. She was also under-18s British chess champion
- She has a twin sister, Maria, and is older by 15 minutes. They are the first set of twins to be elected as MPs and later became the first twins serving as ministers of state
- Ms Eagle was one of the first openly gay female MPs, when she came out in 1997
- She stood in the deputy leadership contest in 2015 and was also a minister under Gordon Brown
- She represented the Remain side in some of the EU TV debates and had also been shadow first secretary of state and had deputised for Mr Corbyn at Prime Minister's Questions
Another potential leadership contender, Owen Smith, said earlier that he was to hold crisis talks with Mr Corbyn to put ideas to him about how to "avert a damaging contest" and a party split.
But Mr Corbyn has said he would not "betray" the party members who elected him last year by standing down.
He has also suggested he would be willing to challenge the executive's decision in court if they say he is not automatically included on the leadership ballot paper.
There is a dispute in the party about whether, as leader, Mr Corbyn would be automatically given a place on a new ballot, or whether he would need the backing of MPs and MEPs to do so.
Anyone wishing to challenge Mr Corbyn needs the backing of 20% of Labour MPs and MEPs - which currently means 51.
Some say Mr Corbyn would also need this backing to be able to stand, but his supporters say he has an automatic place as leader.
A long-standing member of the National Executive Committee, Christine Shawcroft, told the BBC the relevant section of the rulebook refers only to "potential challengers".
And Unite union leader Len McCluskey has said excluding Mr Corbyn would be "a declaration of civil war" and warned of "the mother of all splits" if he is kept off the ballot paper.
But Harriet Harman, former deputy Labour leader, insisted that Mr Corbyn would have to have the support of 20% of the party's MPs to get on a new ballot "because the leader needs to lead an alternative Labour government".
Mr Corbyn received the backing of only 40 MPs in a confidence vote in which 172 expressed opposition to his leadership of the party.
By Ross Hawkins, BBC political correspondent
Jeremy Corbyn has suggested he may go to court if he's not automatically on the ballot paper in Labour's leadership election.
His rivals say he needs the support of a fifth of Labour MPs and MEPs to compete; he says he doesn't.
Two different and completely contradictory bits of legal advice have been obtained. Who's right? This is the key passage in the party rule book:
Do the words "in this case any nomination" apply only to challengers, or do they suggest the sitting leader needs the backing of MPs and MEPs too?
Mr Corbyn's opponents say there is a precedent. When Neil Kinnock - then leader - was challenged by Tony Benn in 1988 Lord Kinnock says he sought nominations.
One barrister active in Labour politics, and a fierce critic of Mr Corbyn, Jolyon Maugham QC, told the Today programme the rules had changed since then and the words above do not force the current leader to find Parliamentary friends.
Don't be fooled into thinking this is just a legal dispute though; the rulebook is another battleground for a bitter political scrap.
Labour's ruling committee, the NEC, will decide and their decision may then be challenged in court.
Whatever the result, the losing side in the dispute won't cheerfully accept it.
Those trying to replace Mr Corbyn argue any leader who can't get the support of 20% - just 51 - of his MPs is a pretty hopeless leader.
The other side say the argument shows the Labour leader's challengers are afraid of a fair fight.