Nearly half of the 331 incumbent Republican senators, House members and governors have condemned the lewd remarks and about 10% have called for Mr Trump to drop out of the race, according to Reuters news agency.
On Monday, Mr Ryan said he would not defend Mr Trump over the remarks.
He told fellow House Republicans he would instead focus on congressional elections to ensure Republicans could maintain legislative control.
Mr Trump fired back in a string of tweets, saying the "shackles" had been removed, allowing him to "fight for America the way I want to". He said he neither wanted nor needed Mr Ryan's support.