The MSNBC host Lawrence O’Donnell retracted a story he reported on Tuesday night that claimed President Trump had made a financial arrangement with so-called Russian oligarchs.

Mr. O’Donnell said the reporting, which he had attributed to a single source on his 10 p.m. program, “didn’t go through our rigorous verification and standards process.”

“I shouldn’t have reported it, and I was wrong to discuss it on the air,” he said on Wednesday, referring to a report he issued on air the night before.

Hours before his broadcast on Wednesday, Charles J. Harder, an attorney for Mr. Trump, had sent a letter demanding that the network and NBCUniversal, its parent company, “immediately and prominently retract, correct and apologize for the aforementioned false and defamatory statements.”