By Nicole Gaouette

(CNN) -- Former ExxonMobil chief executive Rex Tillerson won the backing of the Senate Foreign Relations Committee Monday to be secretary of state when it voted to send his nomination to the full Senate with a recommendation of approval. The vote was 11-10.

Sen. Marco Rubio was a long hold-out and potential "no" vote after he raised concerns about Tillerson's views toward the Russians. But the Florida Republican announced earlier Monday that would support the nomination. If Rubio had voted no, it could have stalled Tillerson, although GOP leaders planned to move him to the floor regardless.

A final confirmation vote on the Senate floor is expected next week, according to leadership aides from each party.

During the vote, Rubio said that he still had reservations about Tillerson, but looked favorably on Tillerson's support for NATO and his recognition that "Russia's claims on Crimea are illegitimate." He came around to supporting the nominee because "given the uncertainty that exists both at home and abroad about the direction of our foreign policy, it would be against our national interests to have this confirmation unnecessarily delayed or embroiled in controversy," Rubio said.

The committee's Republican chairman, Sen. Robert Corker of Tennessee, said "diplomacy has been a critical component" of Tillerson's job at ExxonMobil and praised him as an "adept negotiator" with relationships around the world.

But the Democrats, who voted unanimously against Tillerson, catalogued a series of concerns, including his stance on Russia, human rights, and how long he would recuse himself from decisions that could affect Exxon.

Sen. Robert Menendez, a New Jersey Democrat, said he was troubled by Tillerson's answers on human rights and on ExxonMobil's efforts to avoid or lobby against sanctions on Iran and other countries. "If I am to vote affirmatively for a nominee, I need honest and transparent answers," Menendez said. "I simply do not feel I got them from Mr. Tillerson."

Menendez also returned to a focus of his questions to Tillerson during the hearing last week, saying that "it is incredibly troublesome that Mr. Tillerson and President Trump had not even discussed the specifics of their Russia policy."

Environmental groups and peace advocates expressed dismay at Tillerson's nomination. "If the Senate wanted a human rights-violating, climate-denying, fact-bending chief diplomat, then they got their man," said Friends of the Earth president Erich Pica.

During his confirmation hearing, Tillerson had faced a grilling about his close ties to Russia and whether his business experience could translate into diplomatic skills. His answers about human rights riled both Democrats and Republicans like Rubio, who told the businessman in his confirmation hearing that US foreign policy needs a "moral clarity" he wasn't hearing.

After Rubio met for 90 minutes with Tillerson last week and got answers to more than 100 written questions he'd asked the nominee to answer, the Florida senator said that "despite my reservations, I will support Mr. Tillerson's nomination in committee and in the full Senate."

Rubio was one of just three Senate Republicans who had been withholding support for Tillerson over broad concerns about his ties to Russian President Vladimir Putin. But the two other holdouts -- Sen. John McCain and Sen. Lindsey Graham -- said Sunday they would support Tillerson.

Tillerson's hearing was notable for the number of ways he diverged from Trump on policy questions. The Texan denounced Russian aggression in Ukraine, said he believes climate change is real, advocated for the benefits of the NATO alliance and supported the Trans-Pacific Partnership that Trump pulled the US from by executive order Monday.

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