Rubio -- who refused to say if he would vote for Tillerson after a day of testimony -- pressed the former ExxonMobil CEO hard Wednesday on a slew of human rights questions, pushing him to denounce the behavior of Russia, China, Saudi Arabia and the Philippines and expressing deep disappointment when the Texan refused to do so.

Rubio's vote could make the difference in Tillerson's progress, as Republicans have only a one-vote margin on the Senate Foreign Affairs Committee and Democrats may not support him. But it is possible, should Tillerson stall in committee, for the Senate to bypass the panel and bring the nomination to the full Senate for a vote.

"This is a very important decision and I recognize the partisan split on the committee and what it means," Rubio told reporters after the hearing. "I'm prepared to do what's right."

The Florida senator -- who lost to Trump in the GOP presidential primary and had heated personal exchanges with him during the campaign -- told Tillerson that "moral clarity" is crucial to US foreign policy and expressed disbelief that Tillerson wouldn't deliver judgments on countries' alleged human rights abuses when information is widely available.

"The position you've been nominated to is, in my opinion, the second-most important position of the US government, with all due respect to the vice president," Rubio said.

When the world sees that "the United States is not prepared to stand up and say, yes, Vladimir Putin is a war criminal, Saudi Arabia violates human rights, it demoralizes these people all over the world," Rubio said.

Rubio wasn't alone on the fence. Sen. Lindsey Graham, a South Carolina Republican, said he is also undecided about Trump's choice.

"I think probably what happened today is he is a good man, an honest guy, well qualified in terms of his life experience, but I don't think he grew the vote today," Graham said. "I think there are a lot of Democrats that may have been thinking about voting for him are going to have a harder time of it."

Graham said Tillerson failed to answer a key question at this hearing about what he intends to do about Russian election-related hacking.

"Real fuzzy answer," Graham said. "He needs to clear that up. If he doesn't clear that up, it would be a problem, and I think he can clear it up and he needs to clear it up."

JUST WATCHED Rex Tillerson perfects the non-answer Replay More Videos ... MUST WATCH Rex Tillerson perfects the non-answer 01:18

Tillerson did get one small bit of good news - Sen. James Lankford, a Republican from Oklahoma, indicated on CNN's "Erin Burnett Out Front" that he is "leaning" toward a yes vote on Tillerson, but still wants to review more materials.

During his day-long testimony, Tillerson repeatedly broke with his future boss on key foreign policy issues, backing the Trans-Pacific Partnership, denouncing Russian aggression in Ukraine, and affirming his belief in climate change.

Tillerson said he wasn't against TPP, a massive trade pact that Trump condemned as he made staunch opposition to free trade deals a centerpiece of his presidential campaign.

"I do not oppose" TPP, Tillerson told the Senate Foreign Affairs Committee. "I share some of (Trump's) views regarding whether the agreement that was negotiated serves all of America's interests the best."

Tillerson also blasted Russia's invasion of Ukraine as an "illegal action" -- something Trump hasn't done -- and said he even would have sent the country defensive weapons to use against Moscow.

In a striking exchange, Tillerson admitted that he'd only spoken to the President-elect about world affairs in general terms, and that they haven't discussed Russian policy, telling the Senate panel "that has not yet occurred."

And he took steps in his opening remarks to strike an overall tougher line on Moscow than Trump has to date, saying, "Russia must know that we will be accountable to our commitments and those of our allies, and that Russia must be held to account for its actions."

On climate change, Tillerson told the senators he believes "the risk of climate change does exist and the consequences of it could be serious enough that actions should be taken." In contrast, Trump has in the past described climate change as a hoax perpetrated by China to hurt US manufacturers, although he recently acknowledged the possibility that human activity could be a contributing factor.

He expressed respect for Mexico, calling it "a longstanding neighbor and friend of this country." In sharp contrast to Trump, who said during the campaign that the country sends undocumented rapists and criminals to the US, Tillerson said, "I would never characterize an entire population by any single term at all."

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And he distanced himself from calls to create a registry of American Muslims. "I do not support targeting any particular group," he said.

He also rejected Trump's campaign suggestion that South Korea and Japan should consider developing nuclear arsenals. "I do not agree," he said, adding, "We simply cannot back away from our commitment" to reduce nuclear weapons.

Tillerson encountered repeated challenges from senators on Russia and on ExxonMobil's track record on climate change and the company's opposition to sanctions against rogue regimes.

It was enough, at the hearing's halfway point, for Senate Democratic Leader Chuck Schumer of New York to tweet about the President-elect or "PEOTUS" and his State Department nominee.

"Tillerson hearing raises real questions as to whether PEOTUS & cabinet are prepared to stand up to Putin, Iran & represent US interests," Schumer said.

In a departure from the pattern, Tillerson noted his position on the nuclear deal with Iran was consistent with Trump's. He told senators that while "no one disagrees with the ultimate objective" to stop Iran from getting a nuclear weapon, he feels there should be a "full review of that agreement as well as any number of side agreements that are part of that agreement."

And he echoed Trump's frequent condemnations of China, calling Beijing's attempts to control airspace and its territorial claims "illegal actions." He said China's construction of artificial islands to further its territorial claims were "akin to Russia's taking of Crimea. It's taking of territory that others lay claim to."

Tillerson, who said he hadn't received any classified briefings on the alleged Russian hacks, agreed that it's a "fair assumption" that Putin authorized the attacks.

For weeks, Trump has denied or played down Moscow's involvement in efforts to meddle in the US election, although Wednesday, at a press conference Wednesday, Trump said, "I think it was Russia."

At the hearing, Democrats -- and some Republicans -- came out swinging.

Democrats questioned why in his prepared opening remarks Tillerson didn't mention Russia's alleged hacking of US elections, and they hammered his views on human rights and ExxonMobil's ties to Russia.

Rubio started out by probing Tillerson's views on Russia's violations of human rights and its alleged war crimes in Syria, pointing to information in the public record about civilians being targeted in the Syrian city.

"Is Vladimir Putin a war criminal?" Rubio demanded.

"I would not use that term," Tillerson said. "Those are very, very serious charges to make, and I would want to have much more information before reaching a conclusion."

Sen. Robert Menendez, a New Jersey Democrat, challenged Tillerson on whether his business experience prepares him to represent the US to the world. "Diplomacy is not the same as deal making," Menendez said.

He also cited ExxonMobil's membership in a group that lobbied against Iran sanctions and Exxon's pursuit of a deal in Iraqi Kurdistan despite US opposition. And he brought into the hearing room documents showing millions in dollars of Exxon spending against sanctions on Iran and Russia.

"What message are you now going to be able to send to American businesses who are intent on pursuing their own interests at the expense of US policies and potential political stability in foreign countries," the New Jersey senator asked.

"I have never lobbied against sanctions, personally," Tillerson said. "To my knowledge, Exxon never directly lobbied against sanctions. Not to my knowledge."

"There was lobbying here," Menendez told him. "It's a little amazing that you don't know Exxon was lobbying on these issues."

Maryland Democratic Sen. Ben Cardin later put into the record documents showing Exxon had spent $3.4 million lobbying against the Iran Sanctions Act.

Tillerson also tangled with Virginia Democratic Sen. Tim Kaine over long-standing allegations that ExxonMobil misled the public and its investors about internal research that outlined the threat of climate change. The company's shareholders have filed a class action lawsuit against the company in Texas, and it faces a similar lawsuit in Massachusetts as well.

"Do you lack the knowledge to answer my question or are you refusing to answer my question?" Kaine challenged the nominee.

"A little of both," Tillerson said.