Trump, who is facing an onslaught of criticism from Ryan and other top Republicans for his comments about the Muslim family of a deceased US soldier, thanked Ryan's Republican primary challenger, Paul Nehlen, on Twitter Monday for his "kind words."
"Thanks to @pnehlen for your kinds words, very much appreciated," the Republican presidential nominee tweeted, in what amounts to an extraordinary show of discord between two of the most prominent faces of the Republican Party.
Nehlen, a businessman who like Trump has never held public office, has praised Trump and had recently tweeted articles and comments supporting the GOP nominee.
"My pleasure, Sir. Just want to Make America Great Again," Nehlen responded from his account 10 minutes after Trump's tweet.
Ryan campaign spokesman Zack Roday said their campaign will not "engage in a back-and-forth."
"The speaker is going to remain focused entirely on ensuring we deliver strong Republican majorities this fall," he said.
The Trump campaign did not immediately respond to requests for comment.
Ryan endorsed Trump's presidential bid several weeks after he became the presumptive Republican nominee, but has not hesitated to criticize Trump and express his deep disapproval with some of Trump's more controversial words and proposals.
Ryan reiterated Sunday that he rejects Trump's call for a temporary ban on Muslim travel to the US after Trump took heat for criticizing the parents of Humayun Khan, a US Army captain who died in the Iraq War.
"America's greatness is built on the principles of liberty and preserved by the men and women who wear the uniform to defend it. As I have said on numerous occasions, a religious test for entering our country is not reflective of these fundamental values. I reject it," Ryan said in the statement.
Ryan also criticized Trump's comments questioning a Mexican-American judge's ability to be unbiased in ruling on a lawsuit involving Trump as the "textbook definition of a racist comment."
Ryan has so far refused to withdraw his endorsement of Trump.