International Monetary Fund chief Christine Lagarde warned Wednesday that policymakers on both sides of the Atlantic “should continue to be in crisis management mode” to deal with both the euro-zone debt crisis and the looming U.S. fiscal cliff.

Speaking to reporters at IMF headquarters, Lagarde offered a cautiously optimistic assessment of the euro zone. The recent proposals offered by European leaders in late June to recapitalize Spain’s troubled banking sector, she said, were “a significant variation” from previous steps.

She praised Spain’s efforts to enact structural reforms and said the country needed to find a middle ground between austerity and growth. And she insisted that the IMF would not abandon Greece, which is struggling to bring down its debt load as a condition of its bailout.

“Do we think that this is enough?” Lagarde said. “No. Other steps should be considered.” Specifically, she said, the 17 members of the euro zone needed to continue to integrate their banking sectors and budget policies. She also said that the European Central Bank could do more on monetary policy, given currently low levels of inflation.

Yet Europe, Lagarde stressed, isn’t the only weak spot. Recent IMF projections suggest that the global economy isn’t growing as fast as it did before the crisis. Advanced economies were only set to grow 1.5 percent this year, with emerging economies growing at a disappointing 5.5 percent.

And, she added, there are “serious questions about the U.S. economic future” if policymakers fail to avert a fiscal cliff before January, at which point government spending will drop and taxes will rise sharply.

Lagarde’s remarks on Greece were significant in light of recent reports that the “troika” — the IMF, the European Union and the ECB — was growing weary of the country’s inability to curb its deficit. The Greek parliament is bickering over how to shave $14 billion off the deficit in 2013 and 2014, as a condition of its $160 billion bailout by the troika.

Lagarde dismissed rumors that the IMF would simply give up on Greece. “The IMF never leaves the negotiating table,” she said, adding that Greek efforts to curb deficits since 2009 were “impressive.” Greek authorities, however, needed to do more to crack down on tax evasion, she added.

More generally, Lagarde noted that Europe was suffering primarily from a “crisis of confidence.” As evidence, she pointed to the fact that markets soared last week after ECB head Mario Draghi said he would do “whatever it takes” to strengthen the euro.