The legislation is opposed by President Obama, who says it could complicate negotiations with Iran, the Hill reported Thursday.
Some 53 senators have signed on to the bill, the Library of Congress said in its latest count. It had 26 co-sponsors when it was introduced Dec. 19 by Sens. Robert Menendez, D-N.J., and Mark Kirk, R-Ill.
The House is expected to easily pass the bill if it gets through the Senate. In July, the chamber voted 400-20 to institute new sanctions on Iran's energy section.
In addition, approximately 60 conservative experts and former officials have written to congressional leaders urging rigid parameters be put on any deal with Iran.