"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 BegichPerez creates advisory team for DNC transition The future of the Arctic 2016’s battle for the Senate: A shifting map 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 GrassleyPavlich: The claim Trump let the mentally ill get guns is a lie Congress fails miserably: For Asian-Americans, immigration proposals are personal attacks Grassley, Dems step up battle over judicial nominees MORE (R-Iowa), former committee ranking member Orrin HatchOrrin Grant HatchOvernight Finance: NAFTA defenders dig in | Tech pushes Treasury to fight EU on taxes | AT&T faces setback in merger trial | Dems make new case against Trump tax law | Trump fuels fight over gas tax What sort of senator will Mitt Romney be? Not a backbencher, even day one Lawmaker interest in NAFTA intensifies amid Trump moves MORE (R-Utah) and others, including Sens. Rand PaulRandal (Rand) Howard PaulDem wins Kentucky state House seat in district Trump won by 49 points GOP's tax reform bait-and-switch will widen inequality Pentagon budget euphoria could be short-lived MORE (R-Ky.) and Marco RubioMarco Antonio RubioColbert: Students taking action on gun violence 'give me hope' Lawmakers feel pressure on guns Florida lawmaker's aide fired after claiming shooting survivors were 'actors' 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.