Sen. Ted CruzTed CruzGeorgia campaigns keep up pressure ahead of runoff vote Week ahead in tech: Trump's antitrust pick heads before Senate Week ahead: Senate panel to vote on Trump's FDA pick MORE (R-Texas) on Monday introduced two gun bills, one of which is co-sponsored by a group of 10 Republicans, many of whom signed a pledge earlier this month to filibuster attempts to pass gun control.

The measures provide an alternative to the gun control bill the Senate will begin debate on this week, which would expand background checks on gun purchases, crack down on gun trafficking and beef up security in schools. GOP senators have vowed to block that bill, claiming it goes too far and infringes on the rights of gun owners.

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Cruz introduced a bill to “protect law abiding citizens by preventing criminals from obtaining firearms.” Among the 10 GOP co-sponsors are Sens. Marco RubioMarco RubioTop Trump officials push border wall as government shutdown looms Rubio defends Trump: 'This whole flip-flop thing is a political thing' Rubio: Shutdown would have 'catastrophic impact' on global affairs MORE (Fla.), Rand PaulRand PaulWe can put America first by preventing public health disasters Conservative activists want action from Trump McConnell: 'Big challenge' to pass ObamaCare repeal in Senate MORE (Ky.), and Mike LeeMike LeeTrump takes aim at Obama monuments Trump should work with Congress to block regulations on prepaid cards Sweeping change at DOJ under Sessions MORE (Utah), all signers of the filibuster pledge. Sen. Lindsey GrahamLindsey GrahamFive key moments from Trump's first 100 days GOP senator: There will never be full U.S.-Mexico border wall The Hill's 12:30 Report MORE (S.C.) is also a co-sponsor.

Cruz also introduced an alternative bill aimed at preventing the trafficking and straw purchasing of firearms that does not presently have any co-sponsors.

The text of the bills is not yet available.

A source close to negotiations told The Hill that Republicans are working on further legislation that would focus on enforcing, rather than expanding, the current background-check system and a bill that aims to improve mental health record-keeping.

A focused lobbying effort by families of the victims of the Newtown massacre last week and a background-check deal between Sen. Joe ManchinJoe ManchinPicking 2018 candidates pits McConnell vs. GOP groups Manchin: Trump should make his clothes in West Virginia Sanders supporter to run against red-state Democrat MORE (W.Va.), a centrist Democrat who has an “A” rating from the National Rifle Association, and conservative Republican Sen. Pat Toomey (Pa.) created momentum for gun control legislation last week.

The Senate voted on Thursday to begin debate on the original bill and amendments despite filibuster threats, but the measure still faces an uphill climb. Democrats will need a handful of Republicans to vote in favor of a final bill to send it to the House, but the party can’t count on all of its members to support a final bill.

Cruz spokeswoman Catherine Frazier pointed to the NRA’s decision to grade lawmakers' votes on a procedural motion for the bill — a move that deviates from the group's standard protocol — as evidence the effort “to prevent such legislation is gaining momentum."

Sens. Manchin and Toomey are working to rally support for their background-check provision, and other senators are working on alternative gun bills, including Sens. Chuck GrassleyChuck GrassleyTrump eyeing second Supreme Court seat Grassley: Another Supreme Court vacancy likely this summer Sweeping change at DOJ under Sessions MORE (Iowa) and Graham.

— Updated at 8:08 a.m.