LONDON – The Conservatives captured the largest number of seats Thursday in Britain’s national election but will fall short of a majority — triggering uncertainty over who will form the next government, according to television projections based on exit polls.

An analysis by Britain’s main television networks suggested David Cameron’s Conservative Party will win 307 House of Commons seats, short of the 326 seats needed for a majority.

Polls gave Prime Minister Gordon Brown’s Labour Party 255 seats, and Nick Clegg’s Liberal Democrats 59 seats — far less than had been expected. Small parties got 29 other seats.

The result would bear out predictions that this election would not give any party a majority, resulting in a destabilizing period of political wrangling and uncertainty. Brown could resign if he feels the results have signaled he has lost his mandate to rule, or he could try to stay on as leader and seek a deal in which smaller parties would support him.

The parties immediately began jockeying for position.

Theresa May, a senior Conservative Party lawmaker, said the exit poll result showed Labour’s heaviest losses since 1931, and that the incumbent party had lost “the legitimacy to govern.”

But Labour’s business secretary, Peter Mandelson, pointed out that the sitting prime minister is traditionally given the first chance to form a government.

“The rules are that if it’s a hung Parliament, it’s not the party with the largest number of seats that has first go, it’s the government,” he said. “I have no problem in principle in trying to supply this country with a stable government.”

But he extended an olive branch to the Liberal Democrats, who have called to end the so-called first-past-the-post system, where 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. “First-past the-post is on its last legs.”

The results may yet change. Projecting elections based on exit polls is inherently risky, particularly in an exceptionally close election like this one. Polls are based on samples — in this case 18,000 respondents — and always have some margin of error.