A Republican senator whose vote could be decisive in the confirmation of Supreme Court nominee Brett M. Kavanaugh called their meeting Thursday “an important step,” stopping short of an endorsement after an hour-long discussion of abortion rights, health care and executive power.

Sen. Lisa Murkowski (Alaska), a crucial swing vote with Republicans holding a slim 51-to-49 majority, said she and Kavanaugh had a substantive conversation in their first meeting. She said she looked forward to confirmation hearings next month to learn more.

“What I am seeking is a Supreme Court Justice with the character, the intelligence, and the balance to impartially apply the law to the facts of the case,” Murkowski said in a statement. “Today’s meeting represents an important step in my vetting process. That process, however, has not concluded.”

An abortion rights supporter, Murkowski said ahead of the meeting that Kavanaugh’s position on Roe v. Wade, the 1973 decision legalizing abortion, would be vital to her decision.

Earlier this week, Kavanaugh met with Sen. Susan Collins (R-Maine), who said after their meeting that the judge regarded the decision as “settled law.”

Those words delivered the strongest sign yet that President Trump will probably see the appointment of a second judge in as many years to the nation’s highest court.

Senate arithmetic dictates that favorable votes from Murkowski and Collins will all but guarantee Kavanaugh’s confirmation, with other Republicans in favor. The pair backed the confirmation of Trump-nominee Neil M. Gorsuch to the Supreme Court.

Kavanaugh’s confirmation hearings start Sept. 4. If the three- to four-day schedule proceeds uninterrupted, the GOP should deliver on its goal of having Trump’s pick on the court seated by the time it convenes in early October.

Kavanaugh has faced intense partisan pressure since Trump’s former lawyer Michael Cohen implicated the president in criminal wrongdoing, with Democrats citing his potential role in deciding questions directly related to Trump to call for a delay in the confirmation process. He is accused of holding an expansive view of executive power and a hostile approach toward the indictment of a sitting president, having argued in a 2009 article for the Minnesota Law review that such a process was “badly flawed.”

Democratic senators also stepped up their pressure on Republicans over their failure to release documents from his 35 months as staff secretary to President George W. Bush, saying it had created a “constitutional travesty.” Asked whether he was optimistic about the judge’s prospects of being confirmed amid stern opposition, White House counsel Donald McGahn told The Washington Post: “I’m always optimistic.”

The National Archives hold millions of files relating to Kavanaugh’s career, but Republican senators overseeing the disclosure of documents fear delays to the confirmation process and say that the 184,000 pages of documents from his time working as an associate counsel in the White House and for independent counsel Kenneth Starr are sufficient.

Sen. Charles E. Grassley (R-Iowa), chairman of the Judiciary Committee, has said that the most important documents — among them Kavanaugh’s 300-plus decisions as an appeals court judge — are already public.

Kavanaugh spent Thursday morning and early afternoon meeting senior Democratic senators, who emerged from their meetings unmoved and insistent that more of his papers are released. Sen. Richard J. Durbin (D-Ill.), a member of the Judiciary Committee, immediately emerged from his half-hour meeting to declare that the nominee’s views on impeachment remained unclear and that the “black hole” covering his time in the White House meant it was impossible to further probe his views on executive power and other contentious matters.

With the aid of a calendar in his Senate office, Durbin told reporters: “What you see here in the blacked-out months is what I call the black hole in Brett Kavanaugh’s record.”

“That 35-month period of time — where Brett Kavanaugh served as staff secretary to President Bush — was a period of time that was rife with issues of grave constitutional moment. It’s the reason why the American people have the right to know what he said, how he advised the president, what he wrote,” he said.

Durbin added after their meeting that Kavanaugh had not provided reassurance on whether a sitting president should be culpable for crimes they may have committed. “There is no clarity on his position as to whether or not President Trump in this circumstance would be subject to investigation or prosecution. It’s an unanswered question,” he said.

Sen. Christopher A. Coons (D-Del.) said he understood why people thought Kavanaugh was not being “square” with them, stating: “After what was a vigorous conversation, I know no more about Judge Kavenuagh, his values, his priorities and how he will decide cases. And if I don’t know based on difficulty getting access to documents and difficult getting answers from Judge Kavenaugh about his current views and values, I’m not sure how I will know enough.”

“Stonewalling, declining to answer, being hesitant or being resistant to speak I think is an invitation that leads some of us to conclude that he’s not willing to be square about these issues,” he added.