The Fort Hood Heroes Act would give the victims and their families major benefits and military awards, KXAN-TV, Austin, Texas, reported Monday.
Nearly four years ago, Army Maj. Nidal Hasan opened fire at Fort Hood, killing 13 and wounding 32.
Last week, the U.S. Senate version was announced and the U.S. House version is expected to be introduced this week, the report said.
Rep. John Carter, R-Texas, told KXAN about 25 percent of the House members have signed on as co-sponsors.
Because the Fort Hood attack occurred on U.S. soil, its victims haven't received the same awards and benefits as their deployed counterparts who are wounded or killed either through enemy action in a designated combat zone or in a terrorist attack, Carter said on his website. The Honoring the Fort Hood Heroes Act would correct this and provide benefits to the Fort Hood victims.
"Justice was served when Nidal Hasan was found guilty and handed the death penalty. But justice has not been served for the victims of this horrific shooting," Carter said in a release on his website. "This legislation will ensure the victims of this obvious act of terrorism receive the benefits they not only need, but justly deserve."
Monday's shooting at the Navy Yard in Washington, in which 13 people died, would need separate consideration, even though it is on a military installation, Carter told KXAN, noting the Fort Hood Heroes Act is specifically for Fort Hood, but adding similar consideration could be discussed for future attacks.
"Certainly, it would show that Congress is willing to speak out when they feel an injustice has been done," Carter said.
Notable deaths of 2014 [PHOTOS]