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 during Sunday`s debate for his lewd comments.
The renewed party divisions over Mr Trump come as a new PRRI/Atlantic poll suggested Mrs Clinton holds a 49-38 lead over her opponent.
A video released on Friday revealed Mr Trump describing how he had sought to have sex with a married woman and making other sexually aggressive comments about women.
On Tuesday, President Barack Obama`s spokesman said Mr Trump`s remarks were "repugnant" and amounted to sexual assault.
Nearly half the 331 incumbent Republican senators, House members and governors have condemned Trump`s lewd remarks on the video and about 10% have called for him to drop out of the race, Reuters news agency reports.
Trump Twitter broadside
On Monday, Mr Ryan told fellow House Republicans he would 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 Trump`s conduct and faces a close re-election battle, as "foul-mouthed"
Though the latest revelation underscores a widening divide within the Republican Party, some members insist they are sticking by Mr Trump.
