"Mr. Tillerson has demonstrated he knows the corporate world and can put his shareholders' interests first, but can he be a respected Secretary of State that puts the national security interests of the American people first? It remains to be seen," Cardin said in a statement.
"I look forward to hearing from him on restoring U.S. leadership and countering threats to freedom and peace," Royce said in a statement.
ExxonMobil has extensive drilling interests in Russia and Tillerson has criticized the U.S. sanctions imposed on Moscow over its interference in Ukraine, which have forced the company to abandon some projects.
U.S. business representatives welcomed Trump's selection of Tillerson. The National Association of Manufacturers said it was "pleased that Rex will bring a business perspective to the State Department."
Environmental and human rights groups, meanwhile, denounced the nomination, citing Exxon's environmental record under Tillerson’s guidance and its dealings with an array of governments.
"This sets a very alarming path for the new administration," the international advocacy group Global Witness said in a statement.