Sowing further discord in the Republican Party, GOP nominee Donald Trump said Tuesday that he won't endorse House Speaker Paul Ryan or Sen. John McCain in their respective upcoming primaries.

"I like Paul, but these are horrible times for our country," Trump told the Washington Post in an interview. "We need very strong leadership. We need very, very strong leadership. And I'm just not quite there yet. I'm not quite there yet."

Trump's wording with regards to Ryan is very similar to the way Ryan reacted to Trump winning the nomination back in May: asked in an interview with CNN the week Trump had effectively wrapped up the GOP primary, Ryan said he was "not ready" to endorse Trump.

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"I'm not there yet," he said. (Ryan ultimately endorsed Trump a few weeks later, in early June.)

Ryan is facing a primary challenge from fellow Republican Paul Nehlen, whom Trump thanked and praised on Twitter Monday. That primary is Aug. 9.

As for McCain, Trump insisted in the interview that he's never endorsed the longtime Arizona senator. McCain is facing a three-way race in his Aug. 30 Senate primary, including from state Sen. Kelli Ward.

"I've never been there with John McCain because I've always felt that he should have done a much better job for the vets," Trump said. "He has not done a good job for the vets and I've always felt that he should have done a much better job for the vets. So I've always had a difficult time with John for that reason, because our vets are not being treated properly. They're not being treated fairly."

Ryan and McCain have something in common: both have been publicly critical of the way Trump handled his dealings with the family of Capt. Humayun Khan, a Muslim American soldier who was killed in Iraq in 2004. Khan's parents, Khizr and Ghazala Khan, appeared on stage at the Democratic convention to criticize Trump's rhetoric toward Muslims and proposed immigration ban.

Over the weekend, Ryan issued a statement saying Capt. Khan's sacrifice "should always be honored, period." He did not mention Trump by name in the statement, but his intention was clear.

"Many Muslim Americans have served valiantly in our military, and made the ultimate sacrifice," Ryan said in the statement. "Captain Khan was one such brave example. His sacrifice -- and that of Khizr and Ghazala Khan -- should always be honored. Period."

McCain sharply criticized Trump's handling of the situation, saying Trump does not represent the Republican Party. He has said he will support Trump, but has spoken out against him on this issue and others.

"I cannot emphasize enough how deeply I disagree with Mr. Trump's statement," he said. "I hope Americans understand that the remarks do not represent the views of our Republican Party, its officers, or candidates."

A Ryan campaign spokesman responded to Trump's comments, saying Ryan has never sought the GOP nominee's endorsement.

"Neither Speaker Ryan nor anyone on his team has ever asked for Donald Trump's endorsement," the spokesman said in a statement. "And we are confident in a victory next week regardless."