WASHINGTON — The 30-second video ad released by the Trump campaign last week is grainy, and the narrator’s voice is foreboding. Former Vice President Joseph R. Biden Jr., it says, offered Ukraine $1 billion in aid if the country pushed out the man investigating a company tied to Mr. Biden’s son.

Saying it made false accusations, CNN immediately refused to air the advertisement.

[Related: What the 2020 candidates’ spending on Facebook political ads reveals about their campaigns.]

But Facebook did not, and on Tuesday, the social network rejected a request from Mr. Biden’s presidential campaign to take it down, foreshadowing a continuing fight over misinformation on the service during the 2020 election as well as the impeachment inquiry into President Trump.

In a letter to the Biden campaign, Facebook said the ad, which has been viewed five million times on the site, did not violate company policies. Last month, the social network, which has more than two billion users, announced that politicians and their campaigns had nearly free rein over content they post there.