President Donald Trump said Wednesday that he would "much prefer keeping" Deputy Attorney General Rod Rosenstein, despite reports that the Justice Department official suggested invoking the 25th Amendment last year to remove the president from office.

Trump, during a wide-ranging news conference following a gathering of the United Nations General Assembly, also told reporters that he may delay a scheduled Thursday meeting with Rosenstein to discuss his tenure so as not to interfere with a Senate hearing in which Supreme Court nominee Brett Kavanaugh is slated to confront allegations of sexual assault.

Appearing to offer support for the deputy attorney general, Trump said Rosenstein told him that he did not discuss invoking the 25th Amendment last year while offering to wear a wire to gather evidence of the president's erratic behavior following the abrupt dismissal of FBI Director James Comey.

"He said he never said it, he said he doesn't believe it," Trump said "He said he has a lot of respect for me, and he was very nice and we'll see."

Trump said "I would certainly prefer" not to fire Rosenstein, but he did not make a commitment one way or another before meeting with him face-to-face.

In a sometimes rollicking exchange with reporters on questions about Rosenstein and Kavanaugh, Trump again denied any involvement in Russian efforts to influence the 2016 elections and disputed claims by numerous women that he has committed sexual assault.

"I've had a lot of false charges made against me," Trump said.

The president initially set his meeting with Rosenstein for Thursday, the same day that the Senate Judiciary Committee scheduled a hearing on the allegations against Kavanaugh.

"I may call Rod tonight or tomorrow and ask for a little bit of a delay to the meeting, because I don't want to do anything that gets in the way of this very important Supreme Court pick," Trump said.

The Judiciary Committee plans to hear from Christine Blasey Ford, who has accused Kavanaugh of a sexual assault while in high school. Trump, who has defended Kavanaugh at length, said he did not want to miss Ford's testimony.

Trump scheduled the meeting with Rosenstein to discuss his professional fate – and perhaps the future of the investigation into Russia's election interference in 2016.

Rosenstein was summoned to the White House on Monday, three days after The New York Times reported that the deputy attorney general last year discussed seeking the president's removal from office and proposed wearing a recording device in encounters with the president. The Monday meeting ended with Rosenstein still at his post and a commitment for the Thursday meeting with Trump.

In his capacity at the Justice Department, Rosenstein also oversees special counsel Robert Mueller's investigation into Russia's interference in the 2016 presidential election.

Some Democratic lawmakers have accused Trump of seeking Rosenstein's removal as part of a plan to shut down the Russia inquiry.

Trump and his allies have criticized Rosenstein's performance in office, though some supporters have also warned the president not to fire the Justice Department official now because of the potential political fallout.

Allies such as Fox News host Sean Hannity have accused the FBI of leaking the damaging information on Rosenstein in the hope that Trump would fire him, setting off another firestorm just weeks before elections that will determine political control of Congress.

At his U.N. news conference, Trump again criticized the Russia investigation and said he had nothing to do with Russians who sought to influence the 2016 election by hacking Democrats and pushing fake news.

"There was no collusion, there was no obstruction," he said.

Questions about Rosenstein tenure have swirled since the Times published its report Friday.

Rosenstein, who has repeatedly denied the reports, also contemplated pursuing Trump's removal in the spring of 2017, according to the Times, when the White House had been plunged into chaos following Comey's firing.

Kevin Johnson contributed.