The Countering Iran's Destabilizing Activities Act, which also includes the Russia sanctions, passed the Senate in a 98-2 vote on June 15, as reported by Reuters.
Many lawmakers hoped the bill would become law in time to send a strong message to Russian President Vladimir Putin before President Donald Trump's meeting with him in Germany next week.
But the Senate bill stalled when House Republican leaders said it violated a constitutional requirement that legislation affecting revenues originate in the House, known as a "blue slip" violation.
Lawmakers from the two chambers have bickered about it since. Democrats accused House Republicans of trying to kill the bill to please Trump after administration officials said they had concerns about it. House Republican leaders insisted their objection was solely a procedural one.
"The speaker has made clear that we will take up sanctions once the House receives it," said AshLee Strong, a spokeswoman for Speaker Paul Ryan.
The Senate resolved the procedural issue on Thursday. But the delay means the House will not vote until after the G20, because of Congress' recess next week.
"This is now going to be a referendum on the Republican leadership, if they are going to go along with the president's coddling of Putin and the Russians, then that will have to be their legacy," said Representative Eliot Engel, the top House Foreign Affairs Committee Democrat.
Read alsoBill on new sanctions against Russia adopted in violation of procedure – White HouseEngel and Republican committee chairman Ed Royce have said they want the sanctions passed quickly.
Some House Republicans have reservations. Representative Pete Sessions, whose home state of Texas is central to U.S. energy, said he wanted assurances about how the bill would affect businesses.
Representative Mark Meadows said he would look at the bill closely after hearing from the Italian, German and British ambassadors, who had energy-related concerns.
"It could potentially run into trouble. But it's too early to tell," Meadows said.
The legislation would put into law sanctions previously established via ex-President Barack Obama's executive orders. It includes sanctions on mining and other industries and targets Russians responsible for cyber attacks or supplying weapons to Syria's government.
It also sets up a review process that would require Trump to get Congress' approval before easing sanctions on Russia.