FRANKFURT — Europe is in the midst of a downturn not seen since the end of World War II, and the worst is yet to come, Europe’s top central banker said Thursday as she painted a scenario that will test how far the continent’s political leaders are willing to go to preserve their fractured union.

“The euro area is facing an economic contraction of a magnitude and speed that are unprecedented in peacetime,” Christine Lagarde, the president of the European Central Bank, said as she warned that the eurozone economy could shrink by as much as 12 percent this year.

In a bid to prevent another financial crisis that would generate years of economic woe, the bank’s Governing Council decided Thursday to effectively pay banks to lend money and vowed to do whatever was necessary to counteract the economic impact of the coronavirus pandemic.

But many economists and government leaders agree that despite the central bank’s display of monetary firepower, which could pump more than $4 trillion into the economy, it will not be enough to guarantee the survival of the eurozone without help from governments.