"It's particularly appropriate that the European leaders and in particular President (Nicolas) Sarkozy and Chancellor (Angela) Merkel have decided that things have to really move, and say: something's got to give," Lagarde said in a speech at the European Institute in Washington.
"And this at least beginning of compromise we see gradually shaping up is critical.
"It's not in itself sufficient and a lot more will be needed for the overall situation to be properly addressed and for confidence to return, to not only markets, but to investors, to consumers, to those (companies) that have to set out their strategies for the next two, three or four years," she
Sarkozy and Merkel ahead of a pivotal debt crisis summit had earlier on Monday called for a new EU treaty for either all 27 members or just the 17 eurozone states that would insist on tougher budgetary rules.
Lagarde said the global outlook remained bleak.
"In terms of global economic outlook, we are clearly seeing a situation that can be characterized as extremely serious, extremely concerning, and to use some of Jean-Claude Trichet's own words, extremely grave," she said.
"It's not only serious in the heart of Europe, but it's obviously very serious in many corners of the world."
The IMF last week warned that Europe's worsening economy and financial market turmoil meant it was likely in January to revise downward predictions it made in its World Economic Outlook report issued in October.