"I am pleased to introduce legislation that strikes a balance between states' rights and individuals' Second Amendment rights outlined by the Constitution," Thune said. "Rather than establish a national standard, our bill will ensure that law-abiding citizens are able to carry concealed firearms while at the same time respecting the laws of the respective states they visit."

Thune has introduced similar legislation before, and in 2009 it received 58 votes in support — a majority, but two shy of the 60 votes needed to dodge a filibuster under Senate rules.

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Thune's bill is similar but not identical to legislation that passed the House in November with the support of 40 Democrats, H.R. 822. But Thune's bill is different in that it would allow people from states that allow concealed carry without a permit to also carry without a permit in other states, something the House-passed bill does not allow.

Two Senate Democrats, Mark BegichMark Peter BegichAlaska Senate race sees cash surge in final stretch Alaska group backing independent candidate appears linked to Democrats Sullivan wins Alaska Senate GOP primary MORE (D-Alaska) and Joel Manchin (D-W.Va.), have proposed a Senate companion bill to H.R. 822 that they believe can be passed, in particular because it is more respectful of the rights of states that do have permitting requirements.

A spokeswoman for Begich noted that the National Rifle Association (NRA) supports the Begich bill.

Co-sponsors on Thune's bill include Judiciary Committee ranking member Chuck GrassleyChuck GrassleyNumber of migrants detained at southern border reaches 15-year high: reports Grassley, Cornyn push for Senate border hearing The Hill's Morning Report - GOP pounces on Biden's infrastructure plan MORE (R-Iowa), former committee ranking member Orrin HatchOrrin Grant HatchPress: Forget bipartisanship — it's dead! Privatization of foster care has been a disaster for children Remembering Ted Kennedy highlights decline of the Senate MORE (R-Utah) and others, including Sens. Rand PaulRandal (Rand) Howard PaulAlarm grows over impact of states banning trans youth treatment The Hill's 12:30 Report - Presented by ExxonMobil - World mourns the death of Prince Philip The Hill's Morning Report - Biden assails 'epidemic' of gun violence amid SC, Texas shootings MORE (R-Ky.) and Marco RubioMarco Antonio RubioThe Memo: Biden's five biggest foreign policy challenges Hillicon Valley: Amazon wins union election — says 'our employees made the choice' Overnight Defense: Biden proposes 3B defense budget | Criticism comes in from left and right | Pentagon moves toward new screening for extremists MORE (R-Fla.).

— This story was updated on March 21 to reflect the differences in Thune's bill and the one proposed by Sens. Begich and Manchin.