WASHINGTON — House Democrats put off consideration of Senate-passed legislation to bolster protections for Supreme Court justices a day after a man armed with a pistol, a knife and other weapons was arrested near the Maryland home of Justice Brett M. Kavanaugh.

Democratic aides said the delay would be brief as House and Senate negotiators work through the scope of the added protections and whether the families of clerks would be offered more security. The justices already have security details, but after a draft opinion of a decision overturning abortion rights leaked, the Senate in May unanimously approved the Supreme Court Police Parity Act, which would provide police protection to the immediate families of the nine justices and other officers of the court.

“We had hoped that we could do it today, but we certainly will do it at the beginning of next week,” Speaker Nancy Pelosi, Democrat of California, told reporters on Thursday.

The arrest of Nicholas John Roske, 26, of Simi Valley, Calif., on charges of attempted murder of the conservative justice has added urgency to a measure that was drafted by a Democrat, Senator Chris Coons of Delaware, and a Republican, Senator John Cornyn of Texas. But in the House, it has also become caught in the partisanship of the moment.

Republican leaders accused Democrats on Thursday of worrying only about political violence when it was directed at them, sitting for a month on a bill that could pass the House unanimously. And hours before a prime-time hearing on the Jan. 6 attack on the Capitol by supporters of former President Donald J. Trump, they seemed to attempt to equate the Republican incitement on Jan. 6 with Democratic incitement against Supreme Court justices.

Representative Kevin McCarthy of California, the Republican leader, quoted the Senate Democratic leader, Chuck Schumer of New York, warning the justices in 2020 that “you won’t know what hit you” if the court went ahead with conservative opinions.

“How many times do they have to be threatened?” Mr. McCarthy demanded on the House floor. “How many people need to be arrested with a gun outside their home?”

Senator Mitch McConnell of Kentucky, the Senate Republican leader, said similarly: “No more fiddling around with this. They need to pass it today.”

House Democratic leadership aides painted the delay as a technical, not a political, one, and indicated they wanted a more robust bill than the one passed by the Senate. But they, too, tried to score political points, saying that House Republicans had just voted in near unanimity against gun safety measures sparked by the mass shootings in Uvalde, Texas, and Buffalo, yet had the temerity to feign anger over threats to justices who already had protective details.

The apprehension of a man carrying a “black tactical chest rig and tactical knife,” a pistol with two magazines and ammunition, pepper spray, zip ties, a hammer, a screwdriver, a nail punch, a crowbar, a pistol light and duct tape came at a fraught time, when political violence and gun violence are both prominent issues.

The Jan. 6 hearings begin on the day a leading candidate for the Republican nomination to be Michigan’s next governor was arrested over his participation in the Capitol riot. Moreover, the Supreme Court is expected to decide to overturn not only constitutional protections for abortion but also a New York City law that severely restricts the right to carry guns in public.