The bank said it would loosen its credit standards and buy riskier assets than it had in the past, including Greek debt that was previously excluded because of the government’s low credit rating. By increasing demand, the purchases drive down the interest rates that debt issuers need to pay.

“The Governing Council will do everything necessary within its mandate,” the bank said in a statement Wednesday. “The Governing Council is fully prepared to increase the size of its asset-purchase programs and adjust their composition, by as much as necessary and for as long as needed. It will explore all options and all contingencies to support the economy through this shock.”

Ms. Lagarde’s declaration that there are no limits to what the central bank is willing to do was reminiscent of her predecessor Mario Draghi’s vow in 2012, during a severe debt crisis, to do “whatever it takes” to preserve the euro.

“This is a strong signal from the Europeans that they see the situation in financial markets and are trying to calm things down,” said Torsten Slok, chief economist at Deutsche Bank Securities in New York. “It really is ‘whatever it takes.’”

Ms. Lagarde has been under fire since she made a remark at a news conference last week that was interpreted as a sign she was less willing than Mr. Draghi was to defend Italy and other eurozone members from financial market turmoil. Although Ms. Lagarde quickly walked back the comment, and other high-ranking officials at the bank have spent the last few days emphasizing their resolve, investors continued to pummel bonds issued by Italy, Greece, Spain and other countries considered to be riskier bets.

The size of the stimulus package announced Wednesday, which the European Central Bank called the Pandemic Emergency Purchase Program, or PEPP, seemed intended to discourage investors from betting against the euro.

“We couldn’t hope for more,” Frederik Ducrozet, an economist at Banque Pictet & Cie, wrote in a research note. “Provided the fiscal response continues to build up, this looks like a game-changer for the euro area economy and markets.”