Treasury Secretary Timothy F. Geithner returned Thursday from a three-day, five-city whirlwind tour of Europe and said he was optimistic that the continent’s political and economic leaders would do what’s necessary to arrest their financial crisis as they continue meeting on Friday.

Geithner endorsed proposals by France and Germany to more tightly integrate how the 17 members of the euro-zone currency union make decisions about taxation and spending.

He also expressed confidence that Europe’s leaders would strengthen an expensive effort to head off financial crises facing nations like Italy and Spain, while those countries, with new technocratic governments, would introduce reforms to show they are on a more sustainable financial path.

“The leaders of Europe are moving this week . . . to build the framework for further fiscal and financial integration, which is a very important requirement for the viability of the monetary union,” Geithner said in Milan on Thursday before leaving for Washington. “These are vital and critical but also very challenging reforms, and they will take time. But I think the world can be encouraged by the progress these last few weeks.”

Geithner’s trip began in Frankfurt on Tuesday morning, where he kicked off a series of meetings with political leaders, finance ministers and central bankers from Germany, France, Italy and Spain.

Joined by Treasury Undersecretary for International Affairs Lael Brainard and Deputy Assistant Secretary Christopher Smart, Geithner met with European Central Bank President Mario Draghi, German Finance Minister Wolfgang Schauble, French President Nicolas Sar­kozy, Spanish Prime Minister-elect Mariano Rajoy Brey and Italy’s new prime minister, Mario Monti, among others.

The trip carried diplomatic risks; Geithner originally didn’t plan to hold any news events, which could invite backlash from Europeans sensitive about American meddling. But several counterparts asked for Geithner to appear in public with them.

Monti said after the meeting with Geithner that the U.S. Treasury secretary, “besides holding this important position that he holds, has very wide experience and also wisdom on economic issues. That is why he has been very useful, and it has been very useful to listen to his advice and views.”

A senior Treasury official said Geithner took the trip, at the request of President Obama, to gather insight into what European leaders think is possible ahead of the summit and to remind officials of various U.S. proposals for how best to arrest the crisis. Geithner was also trying to determine how quickly Europeans could implement the plans under discussion, said the official, who spoke on the condition of anonymity because the meetings were not public.

Ted Truman, a former senior Treasury official, said it will be hard to take full measure of Geithner’s trip until the summit concludes.

“Geithner kept saying that he expected great things and was confident, but that cheerleading in public just complemented his pushing in private for something consequential,” Truman said in an e-mail.

Jacob Funk Kirkegaard, a research fellow at the Peterson Institute for International Economics, said Geithner is doing all he can given difficult constraints.

“The risks of a backlash against U.S. meddling in Europe at this point in time is extremely high, so the fact that he — the U.S. Treasury secretary — travels around to the main euro decision makers to offer backstage constructive advice and policy support is about as much he and the administration can do,” Kirke­gaard said by e-mail.