SAN ANTONIO -- As Donald Trump sinks in the polls and continues to warn his voters that the presidential election is “rigged” against him, Sen. John Cornyn said on Friday that he, too, has concerns about the electoral system.

“Cyber security has obviously been a serious issue and has been for a long time. I do share some concerns about the integrity of the electoral system,” he said, adding that he doesn’t see any “grand conspiracy by state actors to try to disrupt our election system.”

But the Senate’s No. 2 Republican leader stopped short of agreeing with the GOP nominee’s suggestion that a loss in November could be the result of voter fraud.

“There are going to have to be some facts identified to support that conclusion and we’ll just have to wait and see what happens,” Cornyn said.

As recently as this week, Trump told his supporters that the election could be “stolen” from him, calling on them to “watch other communities” for fraud at the polls.

The New York Times reports that Trump -- whose campaign has been in free fall in the wake of shaky debate performances, a video in which he describes forcing himself on women and reports from women claiming he inappropriately touched them -- has repeatedly singled out cities with large African-American populations as he warns the election could be "rigged."

Republicans have passed stringent voter identification laws in recent years to combat what they say is the potential for fraud at the polls -- an issue that Democrats have denounced as a form of discrimination.

But now, an increasing number of Republicans say Trump is going too far with his rigged election rhetoric.

Republican presidential candidate Donald Trump speaks at a campaign rally at the Charlotte Convention Center in Charlotte, N.C., on Friday, Oct. 14, 2016. (David T. Foster III/Charlotte Observer/TNS) (TNS)

Some Republicans have reportedly joined the chorus of Democrats criticizing Trump for promoting conspiracy theories about the election, calling on him to substantiate his claims or produce evidence about voter fraud.

Cornyn sidestepped criticizing Trump in his appearance Friday with Texas Land Commissioner George P. Bush and Republican Congressman Will Hurd, R-San Antonio, in which they unveiled a new grant program to help military members transition to law enforcement roles.

But the senator couldn’t escape questions about the election, which he described as among the nastiest in his political lifetime.

Cornyn expressed optimism that Republicans will retain control of the House and Senate, however, despite predictions from some Democrats that Trump has proven toxic enough to help them retake the majority.

“I don’t think anybody confuses the Republican nominee with a traditional Republican,” Cornyn said of Trump, noting that some polls place Republican Senate candidates ahead of the nominee in their respective states.

Cornyn was among those last week to slam a 2005 video in which Trump bragged about kissing and groping women unlikely to resist because of his celebrity status. But, like many Republicans, Cornyn hasn't withdrawn his support for the presidential contender.

I am disgusted by Mr Trump's words about women: our daughters, sisters and mothers. — Senator John Cornyn (@JohnCornyn) October 8, 2016

On Friday, Cornyn said that’s because he’s respecting the will of the voters.

“My position has not changed,” he said. “I support the nominee of my party, who was not my first choice and obviously was not my second choice, but he is the nominee of my party and that’s more a matter of respect for the voters who cast their ballot for him that I feel an obligation to support the nominee.”

Cornyn reiterated that he’s concerned about potential appointments to the Supreme Court and the effect of another Democratic presidency on regulatory agencies. But regardless of what happens on Nov. 8, he said, “the sun is still going to come up on Nov. 9.”