Geithner will first meet European Central Bank President Mario Draghi and in the afternoon German Finance Minister Wolfgang Schäuble.
In Paris on Wednesday, he will meet French President Nicolas Sarkozy and Finance Minister François Baroin.
Geithner is also expected to press the new leaders of Spain, Mariano Rajoy, and Italy, Mario Monti, to take steps that will give markets confidence that no eurozone country will default, and that the region's banks will stay solvent.
The US Federal Reserve joined with the European Central Bank and others in action to ease dollar funding strains a week ago. Both US President Barack Obama and Geithner have pointed to the option of the ECB backstopping European governments and the banking system, an idea which is viewed by many economists as the key to any comprehensive solution to the crisis, but which it is resisted by Germany.
"In the end, the Europeans hold their fate in their hands, but the problem is their fate is our fate," said Edwin Truman, a former advisor to Geithner at the Treasury who is now a senior fellow at the Peterson Institute for International Economics in Washington.
"There's no doubt that their futzing around for the last two years has adversely affected the US economy – and the world economy. One cannot say that too strongly," Truman said.
ECB under pressure
The US treasury chief began his trip by meeting Draghi. He declined to comment on the talks on leaving the ECB, where he spent more than 1-1/2 hours before heading to meet Bundesbank chief Jens Weidmann.
Geithner has advocated leveraging European bailout funds through the ECB to boost its capacity. Weidmann has led opposition at the ECB to it taking a broader role.
With two new prime ministers in Italy and Spain pushing on with reforms, analysts wonder if the closer fiscal integration being discussed by Sarkozy and German Chancellor Angela Merkel will provide cover for the ECB to step up buying of eurozone government bonds.
Many European officials see bilateral loans to the IMF from wealthier eurozone states and key emerging markets like Brazil or China as a way to boost the Fund's capacity to bail out a larger economy like Italy or Spain.
IMF 'second line of defense'
The Treasury maintains that the IMF's resources are adequate, but now appears to be open to such bilateral loans, particularly from Europe.
The Treasury secretary said that there did not seem to be a case for the United States to try to augment IMF resources with its own funds, and it still sees the IMF as a second line of defense. But the official added that loans from European national central banks could help satisfy demands that the region use more of its own money to tame the crisis.
In effect, Geithner could agree not to block such an effort to boost IMF resources if he were satisfied that European leaders were taking strong enough action. As the largest contributor to the Fund, Washington has effective veto power over major changes to the way it operates.