Rex Tillerson's bid to be US secretary of state has narrowly won approval from the Senate foreign relations committee, which all but assures confirmation of President Donald Trump's choice to be the nation's top diplomat.

Members of the Republican-led committee voted along party lines on Monday to back the former Exxon Mobil chairman following a contentious confirmation hearing nearly two weeks ago that stoked concerns he might not win the panel's recommendation.

But just hours before members cast their votes, Republican Senator Marco Rubio declared his support for Tillerson, backing off from a challenge to the new president.

Rubio said that despite serious reservations about Tillerson, particularly over his views on Russia, he believed a president was entitled to significant deference in assembling his Cabinet.

None of the committee's 10 Democrats voted for Tillerson, citing concerns Tillerson would continue to view the world through the lens of a corporate executive and not the nation's chief diplomat.

Senator Ben Cardin of Maryland, the panel's top Democrat, said Tillerson "equivocated" during his confirmation hearing on questions about human rights, civil society and press and religious freedoms, and repeatedly prioritised "narrow business interests ahead of these core national security interests".

Every nominee for the job going back at least four decades has been approved by overwhelming votes from both sides in the foreign relations committee, as senators have wanted to deliver a bipartisan display of confidence to the nation's top diplomat.

No other nominee since 1977 has received more than two no votes from the committee.