In Detroit, a congressman’s holiday party devolved into chaos and a broken nose after demonstrators protesting the war in Gaza appeared with bullhorns.

In Fort Collins, Colo., the mayor abruptly ended a meeting during which protesters demanding a cease-fire in Gaza glued their hands to a wall.

And in places as disparate as a historic church in South Carolina and Radio City Music Hall in Manhattan, President Biden has been heckled and drowned out by demonstrators objecting to his support for Israel.

Protests over the Biden administration’s handling of the war are disrupting the activities of Democratic officials from city halls to Congress to the White House, complicating their ability to campaign — and, at times, govern — during a pivotal election year.

Mr. Biden successfully avoided a messy primary fight, facing no viable opposition within his party. But the Gaza conflict has stoked intraparty tensions nonetheless, raising Democratic concerns that a sustained movement protesting a war thousands of miles away could depress turnout at home in November.

“If you are now organizing people to walk away from supporting the president, then you are now de facto supporting and helping Trump,” Senator John Fetterman of Pennsylvania, a Democrat who has disappointed progressives with his unflinching support of Israel, said in an interview this past week. “If you’re going to play with fire that way, then you need to own the burn.”