US attitudes towards climate change are in the process of “a quantum shift,” Tony Blair said on Saturday, arguing that the world may be “on the verge of a breakthrough” on the issue.

The UK prime minister’s optimism was echoed by John McCain, the Arizona senator and likely US presidential candidate. “I think the US Congress will act soon on this issue and I think the administration will also,” he told the World Economic Forum in Davos, where he was speaking after Mr Blair.

“I admit it’s very late,” Mr McCain said, but he rejected accusations of failed US leadership on climate change and other multilateral issues and highlighted US frustration at other countries’ failure to participate in the campaign against the Taliban in Afghanistan.

“America’s first choice will always be to have an alliance,” he added. Mr Blair’s speech to the Forum’s audience of political, business and non-governmental leaders called for a “muscular” multilateralism to turn political will on climate change, Africa and the Doha trade round into action. “We’re woefully short of the institutions to make multilateralist action effective,” he said.

There was “a yawning gap between our description of an issue's importance and the matching capability to determine it.” Mr Blair highlighted the United Nations Security Council, saying it would “lose legitimacy” without members such as Germany, Japan, Brazil and India, arguing that “a strong transatlantic push” to reform the institution was “long overdue.”

He repeated his argument that there was a “powerful case” for merging the International Monetary Fund and the World Bank and called for changing the rules of European Union.

Mr Blair, who has said he will step down this year, adopted a valedictory tone, referring repeatedly to the lessons he had learned after 10 years in power and defending the principle of intervention – a controversial aspect of his legacy because of his support for the Iraq war.