If the group moves the meeting, Dallas could lose up to $40 million from the 80,000 members attending, USAToday reported.
The NRA responded after Caraway’s request.
Andrew Arulanandam, a spokesperson for the NRA, told WFAA, "No politician anywhere can tell the NRA not to come to their city. We are already there. Dallas, like every American city and community, is populated by NRA members. Our members work in fire stations and police departments. They save lives in local hospitals and own businesses in communities, urban and rural, throughout the country."
Fox News reported that Caraway is a gun owner who says he believes in the Second Amendment, but is challenging the NRA to come to the table to work with leaders to increase gun safety through laws.
The NRA has come under fire after the Feb. 14 shooting in Parkland, Florida where 17 students and teachers were killed and more than a dozen were wounded, NBC News reported.
The gunman, who is 19 years old, owned 10 rifles, CNN reported. He was able to buy them legally, Fox News and The Associated Press reported. That was despite having previous treatment at a mental health clinic and comments on YouTube, attributed to him, that he was going to be a professional school shooter, the AP reported. The FBI said it couldn't confirm who posted the comment, the AP reported.
Last year, the NRA held its annual convention in Atlanta. President Donald Trump was a keynote speaker during the meetings, The Atlanta Journal-Constitution reported.
Florida Gov. Rick Scott was also a speaker at last year's meetings. He currently has an A-plus rating by the NRA, which helped him get re-elected last year, The Tampa Bay Times reported.
Students and their families who were directly affected by last week’s shooting are now speaking out against Scott and anyone who has been backed by the NRA.
Emma Gonzalez, a student at Marjory Stoneman Douglas High School, according to the Tampa Bay Times, said that, "These people who are being funded by the NRA are not going to be allowed to remain in office when midterm elections roll around. They're going to be voted out of office."
WATCH: Florida High School Shooting Survivor Talks About NRA
This year's event guest speakers include NRA CEO Wayne Lapierre, NRA-ILA Executive Director Chris Cox, Sen. Ted Cruz, R-Texas, Benghazi survivor Mark Geist, Rep. Richard Hudson, R-N.C. and political commentator Tomi Lahren.