Just when central bankers thought they were about to get out of the business of emergency economic stimulus, jittery financial markets are threatening to pull some of them back in.

For the European Central Bank, the latest threat requiring vigilance is political turmoil in Italy that's reviving memories of the debt crisis that threatened to fracture the euro area. The Bank of England's path is complicated by Brexit and, across emerging markets, central banks are trying to push back against the strong dollar.

The Federal Reserve is a bit of an outlier — it's already well along its plans to normalize rates in the U.S. and investors still see a hike in mid-June as a virtual certainty. But beyond that meeting, the market turbulence from Italy is clouding the outlook for further Fed rate increases, if you look to the futures market.

The problem for policymakers everywhere is the uncertainty about Italy's prospects may drag on for months until another election is held, possibly in September. That vote, which may be perceived as a referendum on the country's European future, could even have repercussions for the Fed's plans to raise rates in the second half of the year.

"September has become the question mark" for the Fed, said Paul Richards, president of Medley Global Advisors, a policy research firm. "Now you've got this whole bunch of geopolitical risk. They, and the ECB in October, are going to have to make decisions, right at the time you're going to have Italian elections. This geopolitical risk is really going to start putting September in question."

For now, eyes are turning to the ECB as the political struggles in Italy worsen and populist parties begin mobilizing for another election campaign. That sent note yields surging to levels not seen since 2012.

Markets have stabilized somewhat throughout the week. And policymakers shouldn't get lured into hasty action on Italy because of stress in the markets, according to Angel Gurria, the head of the Organization for Economic Cooperation and Development.

If the market ructions increase borrowing costs and tighten financial conditions, that could feed into the broader European economy, hurting confidence and demand. With the euro-area economy already cooling, that could influence the ECB's debate on the winding down of asset purchases, due to happen this year.

Meakin and Miller write for Bloomberg.