Several other Trump cabinet picks are scheduled to receive votes in Senate panels today. If they pass favorably out of committee, as expected along party lines, they head to confirmation votes by the full Senate.
The nomination of Tillerson, the former chief executive of ExxonMobil who has never served in government, advanced by a vote of 56 to 43, with four Democrats joining all 52 Republicans in support.
"He has the type of international work experience that will serve him well as the next secretary of state," Republican Senate Majority Leader Mitch McConnell said.
The White House has accused Senate Democrats of obstruction, and the new president lashed out at the opposition party late Monday, writing on Twitter that Democrats were "delaying my cabinet picks for purely political reasons."
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"They have nothing going but to obstruct," Trump said.
The Senate minority leader Chuck Schumer, fuelled by Trump's recent actions including his controversial executive order on immigration, has announced his opposition to most of Trump's cabinet picks, including Tillerson and attorney general nominee Senator Jeff Sessions.
"In his first week in office the president has stomped over our proud American tradition of welcoming immigrants and refugees, trafficked in alternative facts, and is attempting to fill his cabinet with billionaires and bankers," Schumer said.
With just three of Trump's cabinet members in place so far -- Secretary of Defense James Mattis, Homeland Security Secretary John Kelly and CIA chief Mike Pompeo, plus cabinet-rank US ambassador to the United Nations Nikki Haley -- Republicans have sought to speed confirmation of Trump's other nominees.
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