President Obama and German Chancellor Angela Merkel played down their differences Tuesday over the military campaign in Libya and the flagging European economic recovery, offering assurances that they share the goals of pushing Moammar Gaddafi from power and restoring the global economy.

In a news conference following morning meetings at the White House, the two agreed that Germany would play a large role in Libya following Gaddafi’s ouster, an outcome both suggested is inevitable despite the hard fighting on the ground.

Merkel refused to deploy German military forces to the NATO-led mission, although she recently dispatched additional surveillance aircraft to Afghanistan to free up international assets there for the Libya fight. Obama thanked Merkel for doing so, and said he expected more help once the campaign is over.

“There is going to be a lot of work to do when Gaddafi does step down, in terms of getting the Libyan people back on their feet,” Obama said. “And my expectation is going to be that there will be full and robust German support.”

Merkel’s visit, capped with a state dinner, marks the 10th time she and Obama have met since he took office. On Tuesday, Obama awarded her the Presidential Medal of Freedom, the highest U.S. honor given to a civilian.

Administration officials have long said that Obama admires Merkel’s focus and candor, even though she has at times criticized the president’s fiscal policies.

As early as June 2009, Merkel, as head of inflation-phobic Germany, was already appealing to Obama to begin scaling back spending that he believed was essential to the global economic recovery. Obama, by contrast, urged Europeans to spend more in order to end the recession.

Those differences have lingered, and Obama warned Tuesday that Greece’s economic problems posed a potentially “disastrous” risk to the world economy. He urged Merkel to push for a resolution of the crisis.

Despite getting a $161 billion international bailout last year, Greece is again nearing default. The nation may run out of money this summer if it does not receive more help from the International Monetary Fund and its European neighbors.

Negotiations over additional help, however, are hung up on Merkel’s insistence that private bondholders share some of the cost.

At their joint appearance, Obama did not explicitly call on Merkel to drop her conditions, which the IMF opposes. But he made clear that the United States views the risk posed by Greece as serious, and he put the onus on Merkel and other European powers to find a solution.

“We think that America’s economic growth depends on a sensible resolution of this issue,” Obama said. “We think it would be disastrous for us to see an uncontrolled spiral and default in Europe, because that could trigger a whole range of other events.”

A Greek default could undermine the health of the banks and other institutions that hold the country’s bonds — including some of Europe’s most important financial institutions and the European Central Bank itself.

The IMF, the ECB and the European Union have tentatively agreed to extend more aid to Greece, if the country’s parliament imposes new austerity measures on an already financially strained public.

Meanwhile, European politicians and financial officials are jockeying over the terms of any new bailout, which may require a commitment of as much as $100 billion from the IMF and European nations.

The IMF’s top official in Greece said Tuesday that the “mixed messages” coming from European politicians were undermining the credibility of efforts to rescue Greece.

At the news conference, Merkel suggested the crisis should be left to the Europeans, saying “each and every one ought to deal with his or her own problems.”

“We in Europe have our hands full already with what we need to do,” she said. “And I’m absolutely convinced that as we shoulder our responsibility and meet our responsibilities, so will the United States of America.”