As sitting prime minister, Brown would traditionally be given the first chance to put together a government. His left-of-center Labour party is seen as a more natural coalition fit with the Lib Dems, the third-place party now thrust into the role of potential kingmaker.
But Clegg said the party that had gained the most seats and the most votes -- the Conservatives -- should have "the first right to seek to govern."
"I think it is now for the Conservative Party to prove that it is capable of seeking to govern in the national interest," he said.
Despite winning the largest number of House of Commons seats in Thursday's election, David Cameron's Conservatives fell short of a majority that only a few months ago was considered inevitable. Labour was on track to lose nearly 90 seats in Parliament but still could govern with the help of the Liberal Democrats. Clegg's party surprisingly failed to capitalize on his stellar TV debate performances, but still could hold the keys to Downing St. for one of the other parties. His support is sure to be contingent on a promise of electoral reform, the Lib Dems' main demand.
With 622 of the 650 seats counted, the Conservatives had secured 292 seats, Labour 251, the Liberal Democrats 52 and smaller parties 27 seats. At least 326 of the House of Commons' 650 seats are needed to form a government.
"The country has spoken -- but we don't know what they've said," former Liberal Democrat leader Paddy Ashdown said, summing up confusion.
Days, and possibly weeks, of political horse-trading could lie ahead -- a prospect that gave the financial markets jitters.
Talks were expected to begin between political players Friday, aided by civil service guidelines detailing how the process should unfold.
Although Britain has no written constitution, senior civil servants have been preparing furiously to lay out the rules and avoid market-rattling uncertainty in the event of a hung parliament. The last time a British election produced such a result was in 1974.
A period of political wrangling and confusion in one of the world's largest economies could unsettle global markets already reeling from the Greek debt crisis and fears of wider debt contagion in Europe. Britain's budget deficit is set to eclipse even that of Greece next year, and whoever winds up in power faces the daunting challenge of introducing big government spending cuts to slash the country's huge deficit.
In London, bond trading started in the middle of the night -- six hours earlier than normal -- as traders tried to make sense of the election results. Britain's main stock index and the pound fell Friday as investors reacted to the inconclusive result against a backdrop of global market turbulence.
In the first minute of trading, the FTSE 100 share index was down 1.3 percent at 5,193 before rallying slightly above 5,200. The British pound traded as low as $1.4449 by late morning, down from $1.51 less than 24 hours earlier.
"It's vital that this political vacuum is filled as quickly as possible," said Miles Templeman, director general of business group the Institute of Directors. "The country simply can't afford an extended period of political horse-trading which delays much needed action to tackle the deficit."
The Conservatives insisted they had been given a mandate by the electorate. Cameron said voters had rejected Brown and his Labour Party.
"Our country wants change. That change is going to require new leadership," Cameron said Friday.
Cameron planned to make a statement at 2:30 p.m. (1330 GMT, 9:30 a.m. EDT), which his party said would outline his plan for "strong and stable" government.
Brown also vowed to "play my part in Britain having a strong, stable" government and indicated he would seek an alliance with the Liberal Democrats, pledging action on election reform -- a key demand of his would-be partners.
Other senior Labour figures also reached out to the Liberal Democrats Friday in hopes of blocking Cameron. Foreign Secretary David Miliband said, given the election results, Labour and the Liberal Democrats were "honor bound" to talk to each other.
But some Labour allies urged Brown to step down after Labour's worst election showing since the 1980s.
"Gordon Brown should resign with good grace," former Tony Blair media adviser Lance Price told the BBC. "I think if he tries to stitch up a deal, it will look like that, it will look like a stitch up to the electorate."
Turnout for the election -- the closest-fought in a generation -- was 65.2 percent, higher than the 61 percent seen in Britain's 2005 election.
Some polling stations around the country were overwhelmed by those interested in casting ballots, and hundreds of people were blocked from voting due to problems with Britain's old-fashioned paper ballot system.
Anger flared when voters in London, Sheffield, Newcastle and elsewhere complained that they had been blocked from voting as stations closed -- and the head of Britain's Electoral Commission said some legal challenges to results because of blocked votes were likely.
Police had to quell a sit-in protest in east London by 50 angry residents who were denied the chance to vote. Crowds tried to block officials from taking the ballot boxes in Sheffield, as officials struggled to cope with staggering turnout.
Electoral Commission chief Jenny Watson acknowledged that Britain's paper voting system had been unable to cope with a surge of voters.
Former British Home Secretary Jacqui Smith was the biggest Labour lawmaker to lose her seat after being caught attempting to bill the public for porn movies watched by her husband.
But Labour won the northern England seat of Rochdale -- where Brown made the biggest gaffe of the campaign, caught on an open microphone referring to an elderly voter as a "bigoted woman" after she buttonholed him on immigration. Brown later visited her home to apologize.
In the southern England resort town of Brighton, Britain's first-ever Green Party lawmaker, Caroline Lucas, was elected.
The Conservatives were ousted by Labour under Tony Blair in 1997 after 18 years in power. Three leaders and three successive election defeats later, the party selected Cameron, a fresh-faced, bicycle-riding graduate of Eton and Oxford who promised to modernize its fusty, right-wing image.
Under Brown, who took over from Blair three years ago, Britain's once high-flying economy, rooted in world-leading financial services, has run into hard times. In addition, at least 1.3 million people have been laid off and tens of thousands have lost their homes in a crushing recession.