Judge Brett M. Kavanaugh said Wednesday that he respected Supreme Court precedents on abortion and insisted he has an open mind on whether a sitting president can be indicted.

But he refused to recuse himself from any cases involving President Trump. To make such a commitment now, he said, would be the equivalent of taking a stand on the case itself, which would be inappropriate both for a nominee and for his role as a judge on the U.S. Circuit Court of Appeals for the District of Columbia.

“I should not and may not make a commitment about how I would handle a particular case,” Judge Kavanaugh told the Senate Judiciary Committee, which conducted the first of two days of questioning that will decide whether he wins confirmation to the Supreme Court.

Judge Kavanaugh left every impression that he is willing to rule against Mr. Trump when the law demands it, pushing back against Democrats’ claims that he would be a guaranteed vote for the president’s positions.

“I’m an independent judge. For 12 years, I’ve been deciding cases based on the law and the precedent in each case. If confirmed to the Supreme Court, that’s how I’ll do it as well,” he said. “The person who has the best arguments on the law and the precedent is the person who will win with me.”

He also denied knowledge of sexual harassment by a judge he clerked for 27 years ago, denied knowing about emails purloined by a staffer from Senate Democratic computers 15 years ago and denied having been recruited by the Federalist Society to be Mr. Trump’s nominee.

The lack of major hiccups in Wednesday’s hearing bored the cable news networks, which by the middle of the afternoon had ditched their full coverage of the hearing in favor of their regular programming and commercial breaks.

Mr. Trump pronounced himself “happy” with the hearings. He praised the judge for “some incredible answers to very complex questions.”

“Great intellect, great talent, a great judge, and I would suspect he will be approved very quickly after we’re finished with the hearing,” he said.

Democrats, though, pronounced themselves frustrated with the judge, who they hoped to spar with over gun control and pin down on abortion.

One Democrat accused Judge Kavanaugh of using a “code word” to signal he would overturn Roe. v. Wade, the 1973 Supreme Court decision that established a national right to abortion.

“You were telling the Trump administration that if they wanted someone who would overturn Roe v. Wade, you would make the list. These were your bumper stickers in that campaign,” said Sen. Richard Blumenthal, Connecticut Democrat.

The suspected code word was Judge Kavanaugh’s use of the phrase “abortion on demand” inside an opinion on illegal immigrant teens’ access to abortion in the U.S.

The judge said he wasn’t using a code but rather citing a key phrase from a concurring opinion in the Roe decision.

Throughout the hearing, Judge Kavanaugh kept a worn pocket-sized version of the Constitution handy. He waved it frequently as he answered questions.

He also ticked off favorites from the Federalist Papers, citing James Madison’s No. 39, which lays out the balance of powers between states and the national government, and No. 78, which captured Alexander Hamilton’s vision of a robust and independent judiciary.

The judge also offered four Supreme Court rulings that he called the “great moments in American judicial history”: Marbury v. Madison, in which the judiciary claimed powers to decide constitutionality of laws; Youngstown Steel, in which the court laid out rules for fights between Congress and the presidency; Brown v. Board of Education, which overturned segregation; and U.S. v. Nixon, in which the court ordered the president to comply with a subpoena for Oval Office tapes.

Judge Kavanaugh called the Brown decision the greatest of them, but it was the Nixon case that had more relevance for his confirmation, with the current president facing questions over whether he can be forced to comply with a criminal investigation.

Democrats said Mr. Trump has multiple legal entanglements that could reach the high court, including constitutional challenges to his continuing to receive remuneration from his business empire, the special counsel’s investigation into Russian meddling in the 2016 election and questions over campaign finance violations.

The president’s former personal attorney pleaded guilty this summer to breaking campaign laws, saying he did so at Mr. Trump’s behest.

That makes the president an unindicted co-conspirator, said Mr. Blumenthal, Connecticut Democrat. He said that taints the president’s nomination of Judge Kavanaugh and means the judge should recuse himself from Trump-involved cases.

“It’s unprecedented for a Supreme Court nominee to be named by a president who is an unindicted co-conspirator,” the senator said.

Judge Kavanaugh declined to commit to recusal.

“I should not and may not make a commitment about how I would handle a particular case,” he said, adding that decisions on whether to sit or recuse himself were included in that policy.

Mr. Blumenthal said he was “troubled and disturbed” by Judge Kavanaugh’s answer.

Outside the committee room, Democrats continued to face their relative powerlessness in the proceedings.

Minority Leader Charles E. Schumer, New York Democrat, did flex one tool: He shut down the Senate floor for most of the day to protest the hearings. Under Senate rules, committees are restricted in their ability to meet while the chamber is in session.

That rule is regularly waived by consent of both sides — but Mr. Schumer withheld his consent, leaving Republicans with the choice of shutting down the Kavanaugh questions or shutting down the Senate floor.

They chose to shut down the Senate, underscoring the stakes they place on the confirmation of Judge Kavanaugh.

For Democrats, though, tapping every possible tool of obstruction is critical to appeasing liberal activists, who have been disappointed in their senators’ failure to derail the nomination process.

Indeed, one Democratic senator came under fire after she appeared to apologize to Judge Kavanaugh for the repeated protests that interrupted his hearing Tuesday and Wednesday, saying she was “sorry about the circumstances.”

Kevin de Leon, a Democrat who is running against Ms. Feinstein, took to Twitter to blast her for the apology.

“We should be praising the protesters and standing outside with them, not apologizing for their actions,” Mr. de Leon said.

A day earlier, Mr. de Leon tweeted that he was disappointed no Democratic senators were among the 70 protesters arrested for disrupting the hearings.

On Wednesday, dozens more people were escorted out of the hearing room after shrill disruptions.

“Save Roe! Vote No!” shouted one.

• Dave Boyer and Tom Howell Jr. contributed to this article.

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