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Later on Sunday Clegg met Prime Minister Brown, who remains in post until a new government is agreed, for private talks.
Brown, who had returned to London for the talks from his Scottish constituency home, was clinging to the slim hope that he might yet remain in office if he could swing a coalition with the Liberal Democrats and several of the smaller parties in British politics.
His party also clung to the hope of remaining in power through this route, but media reported that senior figures were prepared to ditch Brown as leader and prime minister if that was part of the coalition demands.
The relationship between Brown and Clegg was rumored to be poor. The BBC reported a highly-placed Liberal Democrat source as saying the conversation went badly after Clegg mentioned that Brown should resign, at which point Brown was alleged to have launched into a tirade.
However, both the Liberal Democrats and a spokesman for the prime minister issued press statements on Saturday denying this, and the prime minister's spokesman described the phone conversation as "short but amicable."