The King-Thompson bill will be similar to a Senate gun proposal on background checks, according to CNN.

"Moving forward we will continue working with our colleagues on both sides of the aisle here in the House, and plan on introducing similar legislation to require comprehensive and enforceable background checks on all gun sales with reasonable family and friends exceptions," the congressmen said in a statement.

King and Thompson, who has lead a House Democratic task force on gun control, have been coordinating with Sen. Pat Toomey's (R-Pa.) office in crafting the measure, CNN reported.

Toomey and Sen. Joe ManchinJoseph (Joe) ManchinWashington VIPs gather to celebrate Mark Penn's new book Overnight Defense: Senate sides with Trump on military role in Yemen | Dem vets push for new war authorization on Iraq anniversary | General says time isn't 'right' for space corps Senate sides with Trump on providing Saudi military support MORE (D-W.Va.) announced on Wednesday that they had reached a deal that would require background checks for gun purchases at gun shows, through classified ads and on the Internet.

That deal is likely to be offered as an amendment to a proposal on gun control Senate Majority Leader Harry ReidHarry Mason ReidTrump presses GOP to change Senate rules Only thing Defense’s UFO probe proves is power of political favors Nevada Democrat accused of sexual harassment reconsiders retirement: report MORE (D-Nev.) plans to bring to the Senate floor on Thursday.

“This is an issue which has grabbed hold of the American people. It is an issue, I think, an issue that has to be resolved. And even if it doesn't go down the way I want it to, I think the American people are entitled to a debate,” King said Wednesday in an interview on CNN's "Starting Point."

—This story was updated at 11:51 a.m.