Britain will have its first female prime minister since Margaret Thatcher after Theresa May and Andrea Leadsom made the shortlist on Thursday to be the leader who will guide the country out of the EU.
Cabinet veteran May won 199 votes from the 329 ruling Conservative lawmakers who took part in the ballot for next party leader and prime minister.
Junior energy minister Leadsom, who was only elected to parliament in 2010 and is a virtual unknown to the wider British public, got 84 votes.
The party's 150,000 members will now be able to choose between the two by postal ballot and the winner will be announced on September 9, even as the IMF urged a swift exit to limit damaging uncertainty.
The third challenger, justice minister Michael Gove, who announced his surprise bid last week after initially supporting former mayor of London Boris Johnson for the post, was rejected after winning just 46 votes following accusations of treachery.
"We need proven leadership to negotiate the best deals for leaving the European Union," May said outside the parliament after the announcement.
"This vote shows that the Conservative Party can come together and under my leadership it will," she said.
The new prime minister will have the task of extricating Britain from its 43-year membership of the European Union following the seismic vote in last month's referendum after a bitterly divisive campaign.
May campaigned for Britain to stay in the EU but now promises to respect the referendum result and make Britain the first country to pull out of the 28-nation bloc, while Leadsom was on the "Leave" side.
She has received the endorsement of UK Independence Party leader Nigel Farage and Johnson, who was the favourite to succeed Cameron until last week.
May has said she has no plans to invoke Article 50 -- the formal procedure for leaving the EU -- before the end of the year, while Leadsom has said she wants to do so as quickly as possible.
EU leaders have warned against dragging out the process, a point pressed by Christine Lagarde, managing director of the International Monetary Fund (IMF), in an interview with AFP in Washington.
"The key word about this Brexit affair is uncertainty and the longer the uncertainty, the higher the risk," she said.
"The sooner they can resolve their timeline and the terms of their departure the better for all. It needs to be predictable as soon as possible."
Some Conservative MPs agree -- about 30 have signed a letter organised by former party chairman Grant Shapps calling for a new leader to be installed by the end of July.
The shock result of the June 23 referendum prompted Cameron to resign and sent global stock markets and the value of the pound plunging.
London's FTSE 100 index has recovered but the Bank of England warned this week that the feared risks to financial stability were starting to materialise.
Aberdeen Asset Management on Thursday became the seventh financial group to order a temporary suspension on redemptions from UK property funds after investors rushed to withdraw investments.
Lagarde said Brexit was a "major downside risk" to the world but played down the likelihood of a global recession, saying: "The immediate effects will be on the UK."
May, who has run the Home Office since 2010, is a well-known national figure.
Leadsom, who has never served in the cabinet, secured surprisingly strong support following a sound performance in EU referendum debates.
In a speech in London to a room packed with supporters, Leadsom said her focus would be on "the continued success of the UK economy".
"Prosperity should be our goal, not austerity," the 53-year-old said.
She dismissed predictions that Brexit could spell economic disaster, and said the fall in the pound to a 31-year low against the dollar was good for exports.
She predicted a return to economic growth when the post-referendum figures are published, adding: "I believe we have a great future ahead of us.
"We need to unite. We need to be positive."
In a round of television interviews, she dismissed reports that she had exaggerated her experience in the financial sector before becoming an MP in 2010.
Former Tory leader Michael Howard acknowledged Leadsom's relative lack of experience, but noted Cameron had no experience in government before becoming prime minister.
He threw his support behind her, telling BBC radio: "She's in tune with the majority of people in this country."