"Yet again, Senate Democrats actively withheld information from the rest of the Committee only to drop information at politically opportune moments", the statement said, doubling down on his remarks that Democrats withheld the first allegation against Kavanaugh from Christine Blasey Ford, who went public last week.
The Times did not cite any sources.
Still, the White House and Republicans have cast doubt on Ms Ford's allegations.
Earlier, the panel had given the California professor until 2:30 pm (1830 GMT) to decide whether to appear, after she rejected a Friday evening deadline imposed by the committee's Republican leader, Chuck Grassley.
Ford's attorneys say that several requests they have made of the committee have been refused, such as calling additional witnesses who Ford remembers being at the party, and having the FBI investigate her story.
The White House criticized Ford for allegedly dithering.
Yet Trump said he was in favor of Ford testifying publicly.
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Mayfield caught a pass from Landry on a variant of the Eagles' famous "Philly Special" for a two-point conversion to tie it at 14. Since then, Griffin is no longer a Brown , the Chargers are no longer in San Diego, and the Browns have not won a football game.
"Despite actual threats to her safety and her life, Dr. Ford believes it is important for senators to hear directly from her about the sexual assault committed against her", the lawyers said in a statement.
"TAKE THE VOTE!" Trump tweeted, blaming "radical left wing politicians" for the controversy.
One of the authors behind the latest account into accusations against Kavanaugh, Jane Mayer, told "CBS This Morning" that at a "certain point.there's things people won't say to a reporter that they might feel they need to say to the Federal Bureau of Investigation".
The senior senator for Trump's Democratic foes, Chuck Schumer, called the president's logic a "highly offensive misunderstanding of surviving trauma", while Democratic Senator Dianne Feinstein said: "We must treat sexual assault survivors with respect, not bully or try to silence them".
Hartmann said the committee would begin "looking into the allegations" but would not commit to calling in additional witnesses for the hearing. Unlike many other news organizations, we have not put up a paywall. But after consultation with a lawyer, Ramirez told the magazine she felt confident enough in her recollection that it happened.
"Her name is Elizabeth Rasor, and she was at Catholic University with (Judge), and she said, "I feel a moral obligation to correct the record here, '" Mayer said, paraphrasing her source". "'I can not live in this country if he's in the Supreme Court'".
Soon after, Senate Republicans issued renewed calls to accelerate the timing of a committee vote.