For American policy makers, the impending exit of the United Kingdom from the European Union has introduced a long list of new headaches — and a much shorter list of new opportunities. The best that the Obama administration can hope for may be to soften the economic and political blow from the British vote on Thursday while seizing this opportunity to shore up NATO and other international organizations.

It’s no secret that President Obama — and a succession of US presidents before him — supported British membership in the EU. The union has helped ensure peace on the continent by drawing the once-warring countries closer together economically and culturally. But now British voters, worried that their nation was losing too much sovereignty to the bloc, have chosen a different direction.

That’s their right, as Obama had no choice but to acknowledge in his remarks on Friday. But the British vote does imperil several American interests.

Most immediately, the likely economic slowdown could spread if policy makers aren’t careful. Stock markets plunged on Friday. British voters voluntarily accepted the risk of recession when they voted to leave the union, but now that risk has been inflicted on everyone else too. The Federal Reserve should take interest rate hikes off the table until it’s clear how much the Brexit vote affects the US economy. Another way to ease the economic pain would be for the United States immediately to commence bilateral trade talks with the UK. Before the vote, Obama said that wouldn’t happen — that the UK would go to the “back of the queue’’ — but he should show enough pragmatism to jump at an economic opportunity in both nations’ interests.

Meanwhile, American diplomats will also need to bolster friendships on the continent. The exit of America’s closest international ally is likely to diminish US influence over future EU decision-making. American businesses are dreading the stricter regulation they might face in continental Europe now that the British and their similar values won’t be at the negotiating table.

Thursday’s “leave’’ victory could also inspire copycats. In France, for instance, the leader of the right-wing National Front says France should get a vote next. In the Netherlands, Geert Wilders, leader of the anti-EU Dutch Party for Freedom, wants a “Nexit’’ vote. The United States benefits from a strong and stable EU that is not enmeshed in a constant existential war with itself.

The departure of Britain from the EU could also introduce an element of instability to Northern Ireland, where the United States played a central role in crafting the peace accord. It now seems that the United Kingdom will be convulsed with status questions of its constituent parts — Northern Ireland, Scotland, England, and Wales. It will take watchful diplomacy by the United States and others to ensure that nothing upsets the last 20 years of peace in Belfast.

As the dust settled from the geopolitical earthquake on Friday, a few faint silver linings appeared. If nothing else, the EU’s troubles could make other international institutions more relevant. NATO, the other major pillar of the postwar European order, has shrunk in importance since the Cold War; many European countries don’t even meet their mandated military spending levels. Perhaps the trouble gripping the EU will make it easier to convince European allies to recommit to NATO.

Finally, if things go badly in Britain after the exit, the experience could also provide a sobering warning to the rest of the world about the dangers that can come from indulging atavistic nationalism. The EU debate in Britain — which included silly discussion about bananas, among other frivolities — did not always match the gravity of the decision that faced voters. For relatively prosperous countries like the United States and the United Kingdom, it’s sometimes possible to forget that politics is serious business. Sadly, the UK and the rest of the world is in for a rough spell that may dispel that notion for voters everywhere.