Firms targeted by the new law are those that supply Iran's Revolutionary Guards or help Iran's energy industry. According to the BBC
, the sanctions are also designed to put pressure on Tehran over what the US claims is its nuclear program.
Iran has denied that it has attempted to build an atomic bomb, claiming that its nuclear industry is for peaceful purposes.
On Wednesday, Mr Obama said that "Iran's leaders continue to ignore their obligations", in an apparent reference to Tehran's nuclear activities.
He warned that Iranian leaders would "face growing consequences. That is a promise".
US Secretary of State Hillary Clinton says, "Our efforts to apply pressure on Iran are not meant to punish the Iranian people. They are meant to change the approach the Iranian government has taken toward its nuclear program."
The House of Representatives will soon vote on the bill. If it passes, it will be sent to President Barack Obama to be signed into law.