Sen. Ted CruzTed CruzBudowsky: Trump’s war against truth Five takeaways from Labor pick’s confirmation hearing Republicans should seize the moment and repeal ObamaCare now 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 RubioDem senator: House Intel chairman may have revealed classified info Five takeaways from Labor pick’s confirmation hearing GOP insists FBI probe won’t slow up Trump MORE (Fla.), Rand PaulRand PaulOvernight Defense: Pentagon chief urges Congress to approve budget boost | Senate fight over NATO addition Defying Trump, Freedom Caucus insists it'll oppose GOP ObamaCare replacement ObamaCare repeal faces last obstacle before House vote MORE (Ky.), and Mike LeeMike LeeRepublicans should seize the moment and repeal ObamaCare now ObamaCare repeal faces last obstacle before House vote Live coverage: Day three of Supreme Court nominee hearing MORE (Utah), all signers of the filibuster pledge. Sen. Lindsey GrahamLindsey GrahamGorsuch rewrites playbook for confirmation hearings Dem senator: House Intel chairman may have revealed classified info 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 ManchinRNC drops six-figure ad buy for Supreme Court, healthcare fight Repeal of Obama drilling rule stalls in the Senate Putting coal profits ahead of coal miners 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 GrassleyLive coverage: Day three of Supreme Court nominee hearing Live coverage: Day two of Supreme Court nominee hearing Grassley, CNN host spar over Trump wiretap claims MORE (Iowa) and Graham.

— Updated at 8:08 a.m.