Lawmakers on Thursday strongly hinted that they were no longer interested in giving Mr. Tillerson much additional rope, and the drive in both parties to impose sanctions is a clear outgrowth of the investigations into whether President Trump’s associates had improper connections to Russian officials during the 2016 presidential campaign.
Senator Bob Corker of Tennessee — the committee’s Republican chairman and often a defender of Mr. Tillerson’s approach, to the chagrin of lawmakers in both parties who had hoped to pursue sanctions sooner — said he had seen “no difference whatsoever” in Russia’s conduct, citing its “work against our interest” in Syria.
“Unless he can come in and demonstrably show us — and I don’t think he will be able to, based on the intelligence I’ve read — we are going to move ahead with a Russia sanctions bill during this next work period,” Mr. Corker said of Mr. Tillerson.
Senator Benjamin L. Cardin of Maryland, the committee’s top Democrat, offered an addendum. “We have seen a change in Russia behavior,” he said. “It’s all been bad.”
During the presidential campaign Mr. Trump called the Iran nuclear deal a “disaster” that would eventually allow Iran to produce its own nuclear weapons. But as president he has been loath to make good on his promise to scrap the accord. Should he do so, Iran would be free to resume the production of uranium and plutonium, which are sharply limited under the existing agreement for the next 13 years.
Still, the vote on Thursday underscored the degree to which the broader promise of the Iran nuclear deal has gone awry. President Barack Obama and John Kerry, the former secretary of state, had hoped the deal, while limited to nuclear fuel production, would open a pathway to cooperation between the two countries.
Instead, both countries have retreated to their corners, with the Iranians working in other ways to influence activities in the Middle East, especially by propping up President Bashar al-Assad of Syria. The United States has done nothing to build on the accord, and Mr. Trump just visited Saudi Arabia, heaping praise on a country that has never held an open election and has a human rights record that rivals Iran’s.
Among those who urged senators to reject the sanctions was Mr. Kerry, who negotiated the nuclear deal. “After Rouhani’s re-election, there is much up in the air/room for misinterpretation,” he said in a series of Twitter messages earlier this week. “This is not the moment for a new Iran bill.”
He lost that argument, with many of the Democrats on the committee voting for the sanctions. Mr. Cardin called Mr. Rouhani’s victory “an encouraging vote,” but argued that the new legislation remained essential.
“This bill is surgical,” he said, noting it had been designed to avoid undermining the 2015 agreement. “Just because they entered into a nuclear agreement, we’re not going to permit them to continue to support terrorism.”
Republicans have continued to express concerns about the Obama administration’s efforts. Senator Jim Risch, Republican of Idaho, said the issues addressed in the current bill should have been part of the nuclear agreement.
“We shouldn’t have to do this,” Mr. Risch said, before supporting the measure, adding that “these people are not people who want to get on the international stage and take a place with the rest of the countries that want to see peace and harmony.”
Senator Tim Kaine, Democrat of Virginia, interjected: “These people — that’s a tough, tough phrase,” he said. “We’ve got no beef with Iranian people.”
Mr. Risch clarified that he was referring only to hostile Iranian leaders, not its citizens. “I should have made that clear,” he said.
Mr. Corker suggested that the bill was in fact “very congruent with the will of the Iranian people themselves,” an assertion that a fellow Republican, Senator Rand Paul of Kentucky, disputed.
Later in the meeting, the committee approved a separate measure to boost efforts to counter Russian propaganda and election interference in the United States and around the world.
Some senators made clear that they had expected to take up true sanctions by now.
“This is not a sanctions bill, though many of us wish it were,” Senator Marco Rubio, Republican of Florida, said pointedly. “This is a defensive measure.”
Two committee members — Senator Jeff Flake, Republican of Arizona, and Mr. Kaine — also introduced on Thursday a bill to authorize military force against the Islamic State and other terrorist groups, a move intended to curb executive authority and reassert congressional power over authorization.