The tweets came after several big-name Republicans announced they could no longer support their presidential nominee in the wake of the publication of a 2005 video showing Trump bragging about groping women. Trump apologized for what he called "locker room talk."
On Monday, Ryan said he would no longer defend Trump through the last month of the general election — but he stopped short of rescinding his endorsement of the New York businessman.
In the morning messages, Trump said "the shackles" had been removed and "disloyal" members of his own party are more of an impediment than Hillary Clinton. And in an afternoon tweet, the GOP nominee attacked Sen. John McCain of Arizona — who said Saturday that he would not vote for Trump.
Pundits have warned for some time that the Republican Party could be on the verge of a civil war.
Former House Speaker Newt Gingrich told CNBC on Monday that a "historic" break in the party could be brewing. A Trump supporter, Gingrich said those who are hoping to "manage decay" under a Clinton White House risk a long-term split with elements of the Republican grassroots.
A spokesman for the House speaker said, "Paul Ryan is focusing the next month on defeating Democrats, and all Republicans running for office should probably do the same."
As Trump attacked the speaker's fidelity, Ryan's own Twitter account posted a series of policy discussions on Tuesday morning but nothing about Trump.
During the primary season, Trump rose to prominence by attacking the "establishment" elements of his party, whom he painted as self-serving and unconcerned with the general populace's well-being. That populist tactic had seen less use, however, during the general election as Trump sought to win over moderate voters.
Ryan endorsed Trump in June — weeks after the businessman had become the presumptive nominee.
—CNBC's John Harwood contributed to this report.