Former Trump campaign chairman Paul Manafort continued to lie to the FBI and to special counsel Robert Mueller’s office after his plea deal in September, Mr. Mueller’s office alleged Monday, in what would be a breach of the agreement by a person whose cooperation has been considered a key asset in the probe.

Mr. Manafort, who pleaded guilty to conspiring against the U.S. and obstruction of justice, agreed to cooperate with the probe into Russian interference in the 2016 election, Mr. Mueller’s office noted in a three-page...