Comcast Corp.’s NBCUniversal won’t continue to air a Trump re-election campaign ad on any of its cable networks unless changes are made to the spot, according to a person familiar with NBCU.

The 30-second commercial contains an unsubstantiated claim about former Vice President Joe Biden’s role in the ouster of a Ukrainian prosecutor. The ad, which CNN rejected last week, alleges Mr. Biden, who is vying for the Democratic nomination, promised Ukraine $1 billion to fire a prosecutor looking into a Ukraine gas company with ties...