Television projections based on exit polls suggest the Conservatives won the largest number of seats in Britain's national election on Thursday but will fall slightly short of a majority.British Prime Minister Gordon Brown indicated Friday he might attempt to form a coalition government, seeking to keep his Labour Party in power.RELATEDEditor's Notes: How good a morning for Nick Clegg?The exit polls reflected uncertainty over who will form the next government and Britain's top three parties — the Conservatives led by David Cameron, Labour and the Liberal Democrats — immediately began jockeying to form alliances.Speaking in his home district in Scotland, Brown vowed to "play my part in Britain having a strong, stable and principled government" — the clearest sign yet that he would try to cling to power and seek an alliance with the third-place Liberal Democrats. Brown also pledged action on election reform — a key demand of his would-be partners.An analysis by Britain's main television stations suggested the Conservatives will win 305 of the 650 House of Commons seats, short of the 326 seats needed for a majority. Labour was seen winning 255 seats and the Liberal Democrats 61, far less than had been expected after their support surged during the campaign.If the projections stand, political wrangling and uncertainty is ahead for one of the world's largest economies — a prospect that could unsettle global markets already reeling from the Greek debt crisis and fears of wider debt contagion in Europe.A need for electoral reformConservative leaders were adamant that the results meant Brown must go — but senior Labour figures lost no time in reaching out to the Liberal Democrats in hopes of blocking Cameron.Business Secretary Peter Mandelson of Labour noted that in a "hung parliament" — one in which no party has a clear majority — the sitting prime minister is traditionally given the first chance to form a government.He extended an olive branch to the Liberal Democrats, who have called for an end to the existing system in which the number of districts won — not the popular vote — determines who leads the country."There has to be electoral reform as a result of this election," Mandelson said. The current system, he said, "is on its last legs."But such a coalition might still not work because the projections showed those two parties combined might still fall short of a majority. The gambit would also risk alienating many in Britain, a country without a constitution where political maneuvers are often governed by informal convention.Theresa May, a senior Conservative Party lawmaker, said Brown had lost "the legitimacy to govern.""No way this man, who has failed this electoral task, can contemplate forming a government," Conservative Party chairman Eric Pickles said.Some early indications suggested that the Conservatives may have a chance at defying exit polls and winning a majority. Official results showed large swings to the Cameron camp in a few key constituencies in the normally Labour-dominated northeast. But the Conservatives failed to capture other key targets in central and southern England — an indication that predictions no party will claim a majority are correct.