President Trump, in a joint Tuesday press conference with Poland's President Andrzej Duda, said he feels "so badly" and "terribly" for Supreme Court nominee Brett Kavanaugh, who has been accused of assaulting a woman when they were both in high school.

Kavanaugh and Christine Blasey Ford, the woman accusing Kavanaugh of assaulting her in high school, have been invited to testify before the Senate Judiciary Committee Monday, although Ford has not confirmed whether she will testify. The committee was supposed to take up a vote on Kavanaugh on Thursday, but that was postponed after Ford came forward with her story in an interview with the Washington Post published Sunday.

"I feel so badly for him that he's going through this, to be honest with you, I feel so badly for him," the president said. "This is not a man that deserves this. This should have been brought to the fore, it should have been brought up long ago. And that's what you have hearings for. You don't want until the hearing is over and then all of the sudden bring it up."

Mr. Trump lambasted Democrats for not bringing up the allegation sooner, particularly criticizing Senate Judiciary Committee Ranking Member Dianne Feinstein, D-Calif., who received the allegation initially. Mr. Trump said he would not oppose the FBI opening an investigation into Kavanaugh, but added that's not what the FBI does. The FBI has told CBS News it referred the allegation against Kavanaugh to Kavanaugh's background file, but has not opened any probe.

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"It wouldn't bother me other than the FBI said they really don't do that," Mr. Trump said.

Earlier in the day, during his meeting with Duda, Mr. Trump said he has not spoken to Kavanaugh because he doesn't think that would be a good idea.

"He is an incredible man, he's an incredible intellect...but we feel that we want to go through a process, we want to hear both sides," the president said in his meeting with Duda.

The allegation against Kavanaugh has roiled the confirmation of Mr. Trump's second Supreme Court pick just ahead of November's midterm elections.

Mr. Trump and Duda said they discussed a number of other topics, including trade and national security. Mr. Trump and Duda brought up the possibility of permanent U.S. military bases in Poland, something Duda said he thinks would help deter Russian influence in the region. Duda said he wants the proposed military base in Poland to be called "Fort Trump," to which Mr. Trump nodded.