WASHINGTON (Reuters) - An influential senator said on Thursday some lawmakers are moving forward on new U.S. sanctions to further cut Iranian petroleum sales, but held out the possibility of sanctions relief if Iran lives up to its U.N. Security Council obligations.

"Some of us are moving forward with a new round of sanctions which will require further reduction in purchases of Iranian petroleum," Senate Foreign Relations Committee Chairman Robert Menendez, a Democrat, said at a congressional hearing. "But we are also serious about relief from sanctions if the Iranian government meets it Security Council (responsibilities)."

(Reporting by Arshad Mohammed; Editing by Vicki Allen)