The first two resolutions considered on the Senate floor were offered by unanimous consent. That parliamentary technique allows senators to avoid debate and a roll-call vote, but also empowers a single senator to object and kill the measure.

A bipartisan resolution to commend the Justice Department and reaffirm the Senate’s support for the intelligence community’s findings was blocked when Senator John Cornyn of Texas, the No. 2 Republican in the Senate, objected.

Mr. Cornyn’s move caught the sponsors of the resolution — Senators Flake and Chris Coons, Democrat of Delaware — off guard. It came after Mr. Flake, an outspoken critic of Mr. Trump, delivered an impassioned speech on the Senate floor accusing the president of “giving aid and comfort” to Mr. Putin.

“By choosing to reject object reality in Helsinki, the president let down the free world by giving aid and comfort to an enemy of democracy,” Mr. Flake said. “In so doing he dimmed the light on freedom ever so slightly in our own country.”

Mr. Cornyn said he favored considering new sanctions, “not sort of sense of the Senate resolutions that have no sting or no impact.” Among his other objections was that the measure was largely symbolic — a remark that brought protests from Mr. Flake and Mr. Coons when they greeted reporters afterward.

The chagrined pair said they intended to introduce the measure again next week. Mr. Flake said symbolism was precisely the point.

“This simply says, in a symbolic way, that we in the Senate don’t buy Vladimir Putin’s rejection or his denial of election interference,” Mr. Flake said. “We here in the Senate should stand and say we don’t believe it. We know the intelligence is right. We stand behind our intelligence community. We need to say that in the Senate. Yes, it’s symbolic, and symbolism is important.”