The House on Thursday passed legislation that would allow the government to revoke the tax-exempt status of nonprofit groups it accuses of supporting terrorist entities, despite significant opposition from Democrats who warned that President-elect Donald J. Trump could exploit it to target his political enemies.

The bill, which also waives the tax liability for U.S. hostages while they are in captivity, began as a strongly bipartisan venture. In April, the House overwhelmingly passed identical provisions, and in September, the measure earned the unanimous support of the Ways and Means Committee.

But then Mr. Trump was elected president. And suddenly, what many Democrats had initially regarded as a reasonable tool for targeting terrorist groups began to be seen as a potentially dangerous weapon ripe for abuse by a president bent on kneecapping his rivals.

An array of nonprofit groups on the left began an intensive lobbying campaign to kill the measure, convinced that Mr. Trump would try to use it to wipe them out.

“This is the death penalty bill that we’re considering today, the bill that empowers Donald Trump to extinguish the life of any nonprofit, of any civil society group, which happens to be on his enemies list,” Representative Lloyd Doggett, Democrat of Texas, said on Thursday, warning that Mr. Trump would “use it as a sword against those he views as his political enemies.”

Republican lawmakers argue that Democrats’ fears are overblown and that the bill is necessary to choke off financial pipelines for terrorist entities, frequently citing the example of Hamas.