"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 political mess has legislators divided over meeting place Former GOP chairman Royce joins lobbying shop Lobbying world 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 GrassleyCharles (Chuck) Ernest GrassleyThe Hill's Morning Report - Presented by Facebook - The choice: Biden-Harris vs. Trump-Pence Trump grabs 'third rail' of politics with payroll tax pause On The Money: McConnell says it's time to restart coronavirus talks | New report finds majority of Americans support merger moratorium | Corporate bankruptcies on pace for 10-year high MORE (R-Iowa), former committee ranking member Orrin HatchOrrin Grant HatchBottom line Senate GOP divided over whether they'd fill Supreme Court vacancy  Five takeaways as panel grills tech CEOs MORE (R-Utah) and others, including Sens. Rand PaulRandal (Rand) Howard PaulWatchdog calls for probe into Gohmert 'disregarding public health guidance' on COVID-19 Massie plans to donate plasma after testing positive for COVID-19 antibodies After trillions in tax cuts for the rich, Republicans refuse to help struggling Americans MORE (R-Ky.) and Marco RubioMarco Antonio RubioDemocrats ramp up warnings on Russian election meddling Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump Lincoln Project expands GOP target list, winning Trump ire 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.