Trump, in a barrage of stinging Twitter posts, condemned the Republicans who have backed away from his White House run, deepening a dramatic rift in the party over his struggling campaign for the Nov. 8 election.
"It is so nice that the shackles have been taken off me and I can now fight for America the way I want to," Trump said on Twitter, adding he would engage Democratic rival Hillary Clinton on his own terms.
Describing "disloyal" Republicans as more difficult than Clinton, he said: "They come at you from all sides. They don't know how to win - I will teach them!"
A string of Republican officials and officeholders have distanced themselves from Trump since a 2005 video surfaced on Friday showing him bragging crudely to a reporter about groping women and making unwanted sexual advances.
Despite the turn away from Trump by some elected Republicans, a Reuters/Ipsos poll of likely voters, released on Tuesday, found 58 percent of Republicans wanted Trump to stay atop their party's ticket and 68 percent said the Republican leadership should stand by him.
The poll, which was conducted after the second presidential debate on Sunday, showed Clinton's lead over Trump widening to 8 points from 5 points last week, before the release of the video.
Ryan, the top Republican in Congress, told party lawmakers on Monday he was breaking with Trump and would not campaign for him, all but conceding Clinton would win the presidency. The move angered some Trump supporters, although Ryan said he would not withdraw his endorsement of the New York businessman.
Trump slammed Ryan as a "very weak and ineffective leader" and complained in another tweet that it was hard to do well with "zero support" from Ryan and others.
Ryan's spokesman, Brendan Buck, said on Tuesday that the speaker "is focusing the next month on defeating Democrats, and all Republicans running for office should probably do the same."
Trump also took aim at U.S. Senator John McCain of Arizona, the 2008 Republican presidential nominee, who said on Saturday that he could not vote for Trump.
"The very foul mouthed Sen. John McCain begged for my support during his primary (I gave, he won), then dropped me over locker room remarks," Trump said. There was no immediate reaction from McCain, who secured his primary election win in August.
Many Republicans worry that Trump's chaotic campaign could hurt their chances of holding majorities in the House of Representatives and Senate in next month's election, and will inflict long-term damage on the party.
In an extraordinary party revolt, nearly half of all 331 incumbent Republican senators, House members and governors have condemned Trump's lewd remarks on the video, and roughly one in 10 has called for him to drop out of the race, a Reuters review of official statements and local news coverage indicates.
Unlike Ryan, Republican National Committee Chairman Reince Priebus told RNC members on Monday that the committee, the party's leadership and fundraising arm, still backed Trump, two RNC members told Reuters.
Trump's vice presidential running mate, Indiana Governor Mike Pence, also reinforced his support in television interviews on Monday.
New Jersey Governor Chris Christie, a former 2016 Republican presidential contender who has became a close ally of Trump, also reaffirmed his backing, although he called Trump's comments in the 2005 video "completely indefensible."
Trump, 70, who has portrayed himself as tough on national security, released a hard-hitting television advertisement on Tuesday featuring footage of Clinton, a 68-year-old former secretary of state, stumbling last month after leaving a service commemorating the Sept. 11 attacks. Her campaign said she had been diagnosed a few days earlier with pneumonia.
"Hillary Clinton doesn't have the fortitude, strength or stamina to lead in our world," the ad's narrator says. "She failed as secretary of state. Don't let her fail us again."
Both Trump and Clinton headed to the key battleground state of Florida on Tuesday.
Before her Florida rally with former Vice President Al Gore, Clinton told a Miami radio station that Trump had "insulted everyone."
"People need to understand what's at stake in this election," she told WMBM.
The White House said on Tuesday that Trump's remarks about groping women in the video amounted to sexual assault. President Barack Obama had found the comments repugnant, White House spokesman Josh Earnest told reporters on Air Force One.
Clinton, the first woman to be picked as a presidential nominee by a major U.S. party, tried to focus on Tuesday on issues that could win over undecided women voters, proposing to expand the child tax credit so that more low-income families can benefit and to increase by $1,000 a year the tax credit available to families for each child up to age 4.