Mr Trump also said Republicans were coming at him "from all sides" and their disloyalty was harder to fight than the Democrats.
Mr Ryan is the latest Republican not to back Mr Trump after a 2005 video emerged showing him making obscene comments about groping women.
However Mr Trump has been strongly supported by running mate Mike Pence.
"You have nominated a man for president who never quits, who never backs down. He is a fighter, he is a winner," Mr Pence said at an event in Iowa, praising him for apologising for his obscene comments during Sunday's debate.