Linking his party's performance to the effects of the global credit crunch in Britain, Brown said: "The real test of leadership is not what happens in a period of success but what happens in difficult circumstances."
Amid speculation that Livingstone would be voted out as part of the backlash against the government, Brown said that he had spoken to Livingstone last night and thanked him "for the campaign he has run and the message he has put across".
In all, some 13,000 candidates fought for more than 4,000 seats on 159 municipal councils in England and Wales as well as the 25-member London Assembly and mayoral vote.
With all 159 local council results outside of London counted,
Labour had lost 331 seats and lost control of nine councils to hold
18, while the opposition Conservatives gained 256 seats and boosted
their council tally by 12 to 65.
The poll drubbing, dubbed a "bloodbath" by London's Evening
Standard newspaper and "Black Friday" by others, was the worst for
Labour since the 1960s under Harold Wilson, the then prime minister.
The remainder were not controlled by any single party.
"We had an excellent night... taking far more seats than many of us had thought we might," Teresa May, the Conservative shadow leader of the House of Commons, said.
She said "crucially" they had made breakthroughs in both southern and northern areas where Labour had enjoyed success under Tony Blair, the former prime minister.
"These are very important moves forward for us. We recognise that if the general election isn't for another two years, there's still some hard work to be done.
"But I think this is very good progress we've made and a very good launch for the run-up to the next election."
Some commentators suggested that the results could represent a tipping point for the Conservatives' hopes at the next general election, which must be held before the middle of 2010.
John Curtice, a professor at Strathclyde University, said the results meant the Conservative party was "back in business".
"The Conservatives can win the next election. They are not bound to... but the possibility of the Tories winning the next election is now on the cards."
Brown has been shaken in recent months by poor opinion polls and by legislators' dissent over tax reforms and plans to extend the period of pre-trial detention for terrorist suspects to 42 days.
Most opinion polls have put mayoral candidates Johnson and Livingstone neck-and-neck.