House Majority Leader Steny H. Hoyer (D-Md.). (Alex Edelman/Getty Images)

House Majority Leader Steny H. Hoyer said Tuesday he is putting off a controversial effort to restore yearly cost-of-living increases for congressional lawmakers following a bipartisan backlash at the prospect of hiking lawmaker pay.

“We’re not going to move ahead at this point in time,” Hoyer (D-Md.) told reporters Tuesday, indicating that the annual bill funding the legislative branch would not be taken up this week due to the impasse. “We haven’t resolved the issue.”

Under existing law, lawmakers are entitled to a yearly salary increase to match rising consumer prices, but Congress voted a decade ago, amid the global economic downturn, to block those raises.

Now, with the economy in better shape, Hoyer and others have argued it is time to restore them. They have put forward several arguments in support, including that the cost of living in Washington has dramatically risen over the past decade, that stagnant salaries make congressional service less attractive to nonwealthy Americans, and that staff retention has become an issue because aides’ salaries cannot exceed member salaries.

Hoyer worked with Republican leaders and congressional appropriators to keep language blocking the yearly pay raise off the legislative branch funding bill. But that was met with bipartisan protests from rank-and-file lawmakers — including several Democratic freshmen — who did not want to take a vote that would be seen as raising their own pay.

The bigger issue in recent days has been winning Republican votes, even though top GOP leaders have voiced support for restoring the yearly pay increase.

Asked whether enough GOP members have stepped forward, Hoyer said, “Some are, some aren’t, and discussions are ongoing.” He said the issue could be revisited next month.