The 70-year-old reality TV star, who is facing criticism from all quarters over lewd remarks made in 2005 against women and surfaced recently in recordings, called Ryan, the nation's top elected Republican, a "weak and ineffective leader" and ridiculed the party's 2008 White House nominee John McCain as "very foul mouthed".
In deepening crisis in the party over his candidacy, US media has billed it a "civil war" situation even as the controversial billionaire has remained largely defiant despite poor performance at the crucial presidential debates against Democratic rival Hillary Clinton.
Trump told the Fox News that "the fact is, I think we should get support and we don't get the support from guys like Paul Ryan".
"I'm just tired of non-support and I don't really want his support. This happens all the time -- if you sneeze, he calls up and announces, 'Isn't that a terrible thing'. So look, I don't want his support, I don't care about his support," he said.
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"They'll be there. I would think that Ryan may be would not be there, maybe he will be in a different position," he said and exuded confidence that he would win the November 8 general election against Democratic rival Hillary Clinton.
"I've had a lot of women come up to me and say, 'Boy, I've heard that and I've heard a lot worse than that over my life. If that's what it is going to take to lose an election, that will be pretty sad," Trump said.
"Disloyal Republicans are far more difficult than Crooked Hillary. They come at you from all sides. They don't know how to win -- I will teach them!," he said in a tweet.
"With the exception of cheating Bernie (Sanders) out of the nomination, the Democrats have always proven to be far more loyal to each other than the Republicans!," Trump said.
"It is so nice that the shackles have been taken off me and I can now fight for America the way I want to," the Republican presidential nominee tweeted.