Sen. Ted CruzRafael (Ted) Edward CruzCruz, Ocasio-Cortez efforts on birth control access face major obstacles Ocasio-Cortez and Cruz's dialogue shows common ground isn't just for moderates Ted Cruz, AOC have it right on banning former members of Congress from becoming lobbyists 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 Antonio RubioElection security bills face GOP buzzsaw Election security bills face GOP buzzsaw The Hill's Morning Report — Uproar after Trump's defense of foreign dirt on candidates MORE (Fla.), Rand PaulRandal (Rand) Howard PaulOvernight Defense: Pompeo blames Iran for oil tanker attacks | House panel approves 3B defense bill | Trump shares designs for red, white and blue Air Force One Senate rejects effort to block Trump's Qatar, Bahrain arms sales Senate rejects effort to block Trump's Qatar, Bahrain arms sales MORE (Ky.), and Mike LeeMichael (Mike) Shumway LeeOvernight Defense: Latest on House defense bill markup | Air Force One, low-yield nukes spark debate | House Dems introduce resolutions blocking Saudi arms sales | Trump to send 1,000 troops to Poland Overnight Defense: Latest on House defense bill markup | Air Force One, low-yield nukes spark debate | House Dems introduce resolutions blocking Saudi arms sales | Trump to send 1,000 troops to Poland Senators clinch votes to rebuke Trump on Saudi arms sale MORE (Utah), all signers of the filibuster pledge. Sen. Lindsey GrahamLindsey Olin GrahamTrump wishes 'Happy Father's Day to all,' including 'worst and most vicious critics' Trump wishes 'Happy Father's Day to all,' including 'worst and most vicious critics' Election security bills face GOP buzzsaw 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 ManchinJoseph (Joe) ManchinThe Hill's 12:30 Report — Presented by MAPRx — Trump takes heat for remarks on help from foreign governments The Hill's 12:30 Report — Presented by MAPRx — Trump takes heat for remarks on help from foreign governments The Hill's Morning Report - Trump and House Democrats resume battle 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 GrassleyCharles (Chuck) Ernest GrassleyOvernight Defense: Pompeo blames Iran for oil tanker attacks | House panel approves 3B defense bill | Trump shares designs for red, white and blue Air Force One On The Money: Pelosi says no debt ceiling hike until deal on spending caps | McConnell pressures White House to strike budget deal | Warren bill would wipe out billions in student debt | Senate passes IRS reform bill On The Money: Pelosi says no debt ceiling hike until deal on spending caps | McConnell pressures White House to strike budget deal | Warren bill would wipe out billions in student debt | Senate passes IRS reform bill MORE (Iowa) and Graham.

— Updated at 8:08 a.m.