Nearly half of the 331 incumbent Republican senators, House members and governors have condemned the lewd remarks on the video 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 also attacked Senator John McCain, who has denounced Mr Trump’s conduct and faces a close re-election battle in Arizona, as “foul-mouthed”.
Despite a widening divide within the Republican Party, some members insist they are sticking by Mr Trump.
New Jersey Governor Chris Christie said he was “really disturbed” by Mr Trump’s comments about women but still planned to support him, saying the election was “about bigger issues than that”.
Texas Senator and former rival Ted Cruz also said he would still cast his ballot for Mr Trump, telling a Texas TV station that Mrs Clinton was an “absolute disaster”.
A recent PRRI/Atlantic poll suggested Mrs Clinton holds a 49-38 lead over her opponent.
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Source: BBC