Summers, a long-running critic of the coalition's austerity agenda who has advised Ed Balls, said that Britain should have focused more on restoring growth rather than on cutting the deficit.
"It's several years since the US exceeded its peak GDP before the crisis – that still hasn't happened in the UK."
In a combative exchange during a debate on the future of monetary policy at the World Economic Forum in Davos, the Harvard University President reportedly said according to CNBC and other reporters: "You blew it on stimulating the UK".
Financial Times reporters initially reported that Summers, who was once tipped to take over from Ben Bernanke as chair of the US Federal Reserve, told Osborne he "blew it". However, they later retracted that, but added: "sentiment and spat with Osborne v real".
Chancellor George Osborne fought back, pointing out that the UK had suffered more from the financial crisis than America.
"We did have a much bigger fall in GDP [than in the US], and the impact of the crisis was even harder because our banking sector was a larger share of the economy than in America.
"The great recession in the UK had an even greater effect – and we were one of the worse effected of any of the western economies.
"Without a credible fiscal policy, as many other countries learned in this crisis, you don't have a credible monetary policy and your market rates go up."