Hoyer said House and Senate lawmakers were continuing negotiations about the final wording of the legislation, and that he wanted to see it on the House floor for a vote next week.
After next week, Congress is scheduled to begin a one week-recess.
"It's very important we pass [the Iran sanctions bill] prior to leaving for Memorial Day," Hoyer said.
The sanctions would seek to further isolate Iran by cutting off its supplies of refined petroleum products such as gasoline.
Companies that do business with Iran's energy sector or that assist the Islamic Republic in importing gasoline would be penalized by cutting off their access to the lucrative U.S. market.
Despite Iran's massive oil reserves, the country has limited refining capacity and has to reimport much of the petroleum products its economy requires.
Lawmakers hope that by limiting Iran's ability to access these products, pressure will increase on Iran's government to cease its nuclear program.