Conservative Party Leader David Cameron has said he wants to work together with the Liberal Democrats to tackle Britain's problems.
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The Conservatives made large gains in the UK general election but not enough to gain an overall majority, resulting in the first hung parliament since 1974.
Mr Cameron said today he wanted to make a 'big, open and comprehensive offer' to Nick Clegg's party to form a stable government.
William Hague confirmed that David Cameron had spoken briefly to Nick Clegg this afternoon. He said that Mr Cameron was not excluding the possibility of Liberal Democrat ministers in a future Cabinet.
A Liberal Democrat official told the Press Association that the two men agreed in a 15-minute conversation that they should 'explore further' plans for economic and political reform.
In his earlier speech, Mr Cameron offered an all-party committee of inquiry on political and electoral reform to look at the possibility of changing Westminster's first-past-the-post voting system.
However, he stopped short of promising the immediate legislation on a referendum on voting reform offered by Prime Minister Gordon Brown less than an hour earlier.
Mr Cameron stressed that it was essential that the parties were able to offer leadership to the country.
'Britain voted for change yesterday, but it also voted for a new politics, it did not vote for party political bickering, grandstanding and point-scoring,' he said.
'Our country's problems are too serious, they are too urgent for that. So we must all rise to this occasion, we must show leadership.'
Mr Cameron outlined the areas of policy agreement between the Conservatives and Lib Dems, which he said offered 'a strong basis for a strong government'.
At the same time he stressed that - unlike the Lib Dems - the Tories remained 'completely convinced' that the new government would have to start cutting Britain's record £163bn deficit this year.
Gordon Brown also offers talks
Mr Brown has also offered to hold talks with Mr Clegg on the formation of a new government, if his discussions with Mr Cameron fail to reach an agreement.
Speaking in Downing Street, Mr Brown said he believed discussions on a 'fairer voting system' were 'essential' and he underlined his commitment to putting proposals for reform to the country in a referendum.
But while he said that Mr Clegg and Mr Cameron should have as much time as they needed to complete their discussion, he stressed that all the parties had a responsibility to make the outcome of the election 'work for the national good'.
Mr Brown said he was addressing the country as Prime Minister in a 'position unknown to this generation of political leaders'.
He said he now had a constitutional duty to seek to resolve the situation for the good of the country.
Liberal Democrat leader Mr Clegg said that he believed the Conservative Party should try to form the next British government.
'It seems this morning that it is the Conservative Party that has more votes and more seats though not an absolute majority and that is why I think it is now for the Conservative Party to prove that it is capable of seeking to govern in the national interest,’ Mr Clegg said.
All of the results are in for today, with one poll not taking place until 27 May. Mr Cameron's Conservatives have won 306 seats, but do not have enough seats to command an overall majority in parliament.
Prime Minister Gordon Brown's Labour Party won 258 seats and the Liberal Democrats are on 57, while other parties and independents won 28 seats.
In Northern Ireland, the DUP won eight seats, Sinn Féin has five, the SDLP has three and other parties have claimed the remaining two seats.
Problems at polling stations
Turnout increased after a high-profile election campaign, leaving hundreds of people unable to vote as polling stations struggled to cope with demand.
Over 29.5m people turned out to vote, which is 65.1% of the electorate and an increase of 4% on 2005.
Returning officers in many parts of the country, including London, Sheffield, Manchester, Liverpool and Newcastle, were taken by surprise by the extra numbers wanting to take part in the election.
There were widespread reports of voters facing long queues outside polling stations only to be turned away as ballots closed at 10pm.
In other areas election staff ran out of ballot papers and electors had to wait until fresh ones were delivered - or give up on exercising their democratic rights.
The electoral commission has promised a review of the problems.