Ms. Lagarde’s credibility, a central banker’s stock in trade, hangs on how she handles the crisis with the limited resources at her disposal. The burden on her may be especially heavy because she is the central bank’s first female president.

She has signaled that she understands the urgency of the situation. She told European Union leaders on a conference call late Tuesday that the situation could become as bad as 2008 if governments do not act decisively enough, according to a person familiar with her remarks. The call was first reported by Bloomberg News.

Angela Merkel, the German chancellor, acknowledged during a news conference on Wednesday that Ms. Lagarde had warned of the virus’s consequences. Ms. Merkel said she took Ms. Lagarde’s view of the situation “very seriously.”

But Ms. Lagarde has not committed the E.C.B. to specific measures before the members of the Governing Council have had a chance to debate them, so there remains uncertainty about what they will decide.

Ms. Lagarde is no stranger to crises. As managing director of the International Monetary Fund, she was deeply involved in the eurozone rescue plan in response to the Greek debt meltdown in 2010. But she has no experience as a central banker and, unlike her predecessor, Mario Draghi, does not have a doctorate in economics.

What Ms. Lagarde says at a news conference Thursday may be just as important as what the Governing Council decides. She must allay fears that the central bank is out of ammunition and powerless to calm financial markets.

That won’t be easy. When the Fed cut its benchmark rate by 0.5 percentage points last week, the market rally afterward lasted all of 15 minutes. The E.C.B. has much less room to maneuver than its American counterpart, and the crisis has only grown worse since the Fed acted.