But Mr Brown stressed he was also willing to discuss with Mr Clegg "areas where there may be some measure of agreement" between Labour and the Lib Dems.
These would include plans to ensure "continuing economic stability" and "far-reaching political reforms", Mr Brown added.
And Labour's promise to stage a referendum on any changes to the electoral system remained, he said.
Earlier Mr Brown - who retained the seat of Kirkcaldy and Cowdenbeath in Fife - promised to play his part in securing "a stable, strong and principled government" after the UK election resulted in a hung parliament.
He said he wanted a government which would lead Britain into a "sustained recovery".
In a statement issued earlier on Friday, Mr Brown said it was his duty to "take all steps to ensure Britain has a strong, stable and principled government".
The British people have given him a big thumbs-down. I think the idea that Gordon Brown could stay on is extraordinary
Chris Grayling Shadow home secretary
"This is, of course, chiefly a task for politicians and - in time - for Parliament.
"But to facilitate this process and consistent with the conventions set out in the draft Cabinet Manual, I have asked the cabinet secretary to arrange for the civil service to provide support on request to parties engaged in discussions on the formation of government."
The Tories have 306 seats, which is 20 short of the total needed to secure a majority, while Labour are on 258.
The poll in one remaining constituency -
Thirsk and Malton
- has been delayed until 27 May, owing to the death of the UKIP candidate, John Boakes.
It means the UK now has a hung parliament and Mr Brown continues as prime minister while he decides whether he could form a government, or whether he should allow David Cameron to do so.
Business Secretary Lord Mandelson said it would be "rather a surprising thing" if Mr Brown stood down as prime minister on Friday.
His duty was "to stay at his post, to continue doing his job and not resign until it is clear who the Queen should call as an alternative to form a new government, should Mr Brown not be able to do so", the peer said.
Gordon Brown continues as prime minister
Mr Brown wants to play a role in forming a "strong" government
Schools Secretary Ed Balls retains seat, despite strong Tory challenge
Ex-Home Secretaries Jacqui Smith and Charles Clarke are defeated
Margaret Hodge sees off BNP leader Nick Griffin, who comes third in Barking
"Either there has to be a minority government which tries its chances or a combination of other parties - in this case most likely the Labour Party and Liberal Democrats - would have to see if they can form some arrangement instead," Lord Mandelson added.
But the shadow home secretary, Chris Grayling, said most people would "look at the idea of Gordon Brown still in Downing Street, still trying to hold on to power, as being quite extraordinary".
"He has no mandate," Mr Grayling told GMTV.
"The British people have given him a big thumbs-down. I think the idea that Gordon Brown could stay on is extraordinary."
Most of Labour's cabinet ministers retained their seats, but the Conservatives came within 1,100 votes of defeating Schools Secretary Ed Balls in
Morley and Outwood
in West Yorkshire.
There were defeats for two former home secretaries, however, as Jacqui Smith was beaten in
and Charles Clarke lost in
Labour's Margaret Hodge successfully defended
in east London from a challenge by British National Party leader Nick Griffin, who came third.
She said voters had sent a clear message to the BNP, telling them: "Pack your bags and go."
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