GLEN ELLYN, Ill. -- Ted Cruz suggested on Monday that it would take Donald Trump shooting somebody in New York City to not support the current front-runner in the general election if he becomes the Republican Party presidential nominee.

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"Well I can give you one example where I would no longer support Donald Trump," Cruz told reporters in Rockford, Illinois. "If, for example, he were to go out on Fifth Avenue and shoot somebody, I would not be willing to support Donald Trump."

Reporters pressed Cruz on Monday why he would continue to back Trump despite suggesting over the weekend that Trump "encourages violence" and "disrespects voters."

Since the first GOP debate, Cruz has maintained his commitment to supporting the eventual Republican nominee next November. He continued to hold the line on Monday, telling reporters, "When I tell you I'm going to do something, I'm going to do it."

Cruz continued: "At the outset of this campaign, I committed to support the Republican nominee, and I honor my word. And honoring your word means actually honoring your word. You do what you said you would do."

The Texas senator also said over the weekend that Hillary Clinton "would do even more damage" to the country and be "the lesser of two evils."

His comments Monday referenced a statement Trump made earlier this year, saying his supporters were so strongly behind him that "I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn't lose voters."

Marco Rubio and John Kasich cast doubt this weekend over their own pledges to back Trump after the candidate welcomed violence at his campaign rallies.

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Rubio told reporters earlier on Saturday that it was "getting harder every day" to see him putting his backing behind Trump. And Kasich condemned the "toxic environment" harvested by Trump, adding Trump's recent actions are making it "very extremely difficult" to support him.

Cruz also continued his push on Monday for Rubio and Kasich to leave the race and narrow the field into a head-to-head matchup with Trump - a duel Cruz's campaign believes would allow the Texas senator to still win the GOP nomination outright before this summer's convention.

As part of that call, Cruz told reporters he is open to the pair joining a potential Cruz administration.

"You know, going forward, look, of course, I could absolutely see a place for Marco Rubio and john Kasich in an administration," Cruz said.

Cruz is making a five-stop swing through Illinois before the state's primary on Tuesday.

Ted Cruz on the campaign trail:



27 PHOTOS Ted Cruz on the campaign trail See Gallery Cruz stands by pledge unless Trump shoots someone STAFFORD-MARCH 1: Ted Cruz holds his victory rally at the Redneck Country Club in Stafford, Texas. On the left is his wife, Heidi and their two daughters and on the right is the Lt. Governor of Texas, Dan Patrick. (Photo by Lucian Perkins /for The Washington Post via Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, stands on stage during a Super Tuesday night event in Houston, Texas, U.S., on Tuesday, March 1, 2016. Cruz said Monday in Dallas that Super Tuesday will make the Republican primary a 'two-man race,' predicting that he and Donald Trump will finish far ahead of rivals Marco Rubio, John Kasich and Ben Carson in terms of delegates. Photographer: Matthew Busch/Bloomberg via Getty Images Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, greets attendees with his wife Heidi Cruz and children during a campaign event in San Antonio, Texas, U.S., on Monday, Feb. 29, 2016. Cruz said Monday in Dallas that Super Tuesday will make the Republican primary a 'two-man race,' predicting that he and Donald Trump will finish far ahead of rivals Marco Rubio, John Kasich and Ben Carson in terms of delegates. Photographer: Matthew Busch/Bloomberg via Getty Images *** Local Captions *** Ted Cruz; Heidi Cruz US Republican presidential hopeful Sen. Ted Cruz speaks at a presidential campaign rally in Dallas, Texas on February 29, 2016 one day before the 'Super Tuesday' primaries. Americans in a dozen states head to the polls for a slew of primaries and caucuses March 1 on what is considered the most important day of the presidential nominations calendar. / AFP / Laura Buckman (Photo credit should read LAURA BUCKMAN/AFP/Getty Images) UNITED STATES - FEBRUARY 27: Presidential candidate Sen. Ted Cruz, R-Texas, arrives for a campaign rally near the Georgia State Capitol Building in Atlanta, Ga., February 27, 2016. (Photo By Tom Williams/CQ Roll Call) HOUSTON, TX - FEBRUARY 24: Republican presidential candidate U.S. Sen Ted Cruz (R-TX) greets people during a campaign rally at the Mach Industrial Group on February 24, 2016 in Houston, Texas. The process to select the next Democratic and Republican Presidential candidates continues. (Photo by Joe Raedle/Getty Images) AMES, IA - JANUARY 30: Republican presidential candidate Sen. Ted Cruz (R-TX) arrives at a campaign event at the Gateway Hotel on January 30, 2016 in Ames, Iowa. The Democratic and Republican Iowa Caucuses, the first step in nominating a presidential candidate from each party, will take place on February 1. (Photo by Brendan Hoffman/Getty Images) DES MOINES, IA - JANUARY 31: Republican presidential candidate Sen. Ted Cruz (R-TX) speaks to Iowa voters at the Iowa State Fairgrounds January 31, 2016 in Des Moines, Iowa. The U.S. presidential election kicks off tomorrow with the state's caucuses. (Photo by Win McNamee/Getty Images) HAMLIN, IA - JANUARY 30: Republican presidential candidate Sen. Ted Cruz (R-TX) speaks at a campaign event at Darrell's Place on January 30, 2016 in Hamlin, Iowa. The Democratic and Republican Iowa Caucuses, the first step in nominating a presidential candidate from each party, will take place on February 1. (Photo by Brendan Hoffman/Getty Images) HAMLIN, IA - JANUARY 30: Republican presidential candidate Sen. Ted Cruz (R-TX) (C) greets an audience member as he is introduced at a campaign event at Darrell's Place on January 30, 2016 in Hamlin, Iowa. The Democratic and Republican Iowa Caucuses, the first step in nominating a presidential candidate from each party, will take place on February 1. (Photo by Brendan Hoffman/Getty Images) LAS VEGAS, NV - DECEMBER 17: Republican presidential candidate Sen. Ted Cruz (R-TX) speaks during a campaign rally at the Siena Community Center on December 17, 2015 in Las Vegas, Nevada. Two days after participating in the fifth GOP presidential debate, Cruz began a swing through eight Super Tuesday states in five days. (Photo by Ethan Miller/Getty Images) WASHINGTON, DC - DECEMBER 03: Republican presidential candidate Sen. Ted Cruz (R-TX) leads a moment of silence for victims of the San Bernardino shooting prior to his address to the Republican Jewish Coalition at Ronald Reagan Building and International Trade Center December 3, 2015 in Washington, DC. Candidates spoke and took questions from Jewish leaders and activists. (Photo by Alex Wong/Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, speaks during a Tea Party Patriots rally against the Iran nuclear deal on Capitol Hill in Washington, D.C., U.S., on Wednesday, Sept. 9, 2015. A revolt among U.S. House Republicans delayed action on the Iran nuclear deal today as some members insisted they aren't bound by a Sept. 17 deadline in their efforts to kill the agreement. Photographer: Andrew Harrer/Bloomberg via Getty Images DES MOINES, IA - AUGUST 21: Republican presidential candidate Sen. Ted Cruz (R-TX) speaks to supporters at his Religious Liberty Rally on August 21, 2015 in Des Moines, Iowa. Earlier in the day Republican presidential candidate Sen. Ted Cruz (R-TX) visited and spoke to guests at the Iowa State Fair. (Photo by Scott Olson/Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, speaks at the Iowa State Fair Soapbox in Des Moines, Iowa, U.S., on Friday, Aug. 21, 2015. A day after Jimmy Carter appeared on national television to talk about the cancer that's ravaging his body, Cruz criticized the former president's administration in a speech in Iowa. Photographer: Daniel Acker/Bloomberg via Getty Images Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, eats a pork chop at the Iowa Pork Producers tent during the Iowa State Fair in Des Moines, Iowa, U.S., on Friday, Aug. 21, 2015. A day after Jimmy Carter appeared on national television to talk about the cancer that's ravaging his body, Cruz criticized the former president's administration in a speech in Iowa. Photographer: Daniel Acker/Bloomberg via Getty Images Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, speaks at the Rally for Religious Liberty in Des Moines, Iowa, U.S., on Friday, Aug. 21, 2015. A day after Jimmy Carter appeared on national television to talk about the cancer that's ravaging his body, Republican presidential candidate Cruz criticized the former president's administration in a speech in Iowa. Photographer: Daniel Acker/Bloomberg via Getty Images UNITED STATES - AUGUST 8: Presidential candidate Sen. Ted Cruz (R-TX) spends a few moments with his daughter Catherine before the start of the Cruz bus tour rally in a field behind Sprayberry's BBQ in Newnan, Ga., on Saturday, Aug. 8, 2015. (Photo By Bill Clark/CQ Roll Call) Texas Senator Ted Cruz participates in the Republican presidential primary debate on August 6, 2015 at the Quicken Loans Arena in Cleveland, Ohio. AFP PHOTO / MANDEL NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images) UNITED STATES - JULY 29: Sen. Ted Cruz, R-Texas, awaits for the elevator doors to close as he arrives in the basement of the Capitol, July 29, 2015. (Photo By Al Drago/CQ Roll Call) WASHINGTON, DC - JULY 28: Republican presidential candidate, U.S. Sen. Ted Cruz (R-TX) speaks during a Anti-abortion rally opposing federal funding for Planned Parenthood in front of the U.S. Capitol July 28, 2015 in Washington, DC. Sen. Rand Paul (R-KY) announced a Senate deal to vote on legislation to defund Planned Parenthood before the Senate goes into recess in August. (Photo by Olivier Douliery/Getty Images) WASHINGTON, USA - JULY 23: Republican Presidential Candidate Senator Ted Cruz speaks out against the nuclear deal with Iran during a demonstration that was interrupted by counter protestors in Lafayette Park across the the street from the White House in Washington, DC on July 23, 2015. (Photo by Samuel Corum/Anadolu Agency/Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 U.S. presidential candidate, speaks during The Family Leadership Summit in Ames, Iowa, U.S., on Saturday, July 18, 2015. The sponsor, The FAMiLY LEADER, is a 'pro-family, pro-marriage, pro-life organization which champions the principle that God is the ultimate leader of the family.' Photographer: Daniel Acker/Bloomberg via Getty Images AMES, IA - JULY 18: Republican presidential hopeful Senator Ted Cruz of Texas fields questions at The Family Leadership Summit at Stephens Auditorium on July 18, 2015 in Ames, Iowa. According to the organizers the purpose of The Family Leadership Summit is to inspire, motivate, and educate conservatives. (Photo by Scott Olson/Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, stands outside while waiting to speak during the Faith and Freedom Coalition's 'Road to Majority' legislative luncheon in Washington, D.C., U.S., on Thursday, June 18, 2015. The annual Faith & Freedom Coalition Policy Conference gives top-tier presidential contenders as well as long shots a chance to compete for the large evangelical Christian base in the crowded Republican primary contest. Photographer: Andrew Harrer/Bloomberg via Getty Images WASHINGTON, DC - JUNE 04: Sen. Ted Cruz (R-TX) participates in a Judiciary Subcommittee hearing on the Affordable Care Act on Capitol Hill June 4, 2015 in Washington, DC. The hearing is billed as 'Rewriting The Law, Examining the Process That Led to the ObamaCare Subsidy Rule'. (Photo by Mark Wilson/Getty Images) Senator Ted Cruz, a Republican from Texas and 2016 presidential candidate, speaks during a press conference at the Hampton Inn and Suites in Seneca, South Carolina, U.S., on Wednesday, Feb. 17, 2016. Cruz says Donald Trump sent his lawyers cease and desist letters over a Cruz campaign ad that portrays Trump as pro-choice saying that if the Cruz campaign doesn't pull ad, they'll see immediate legal action to prevent the continued broadcast of this ad, according to Cruz. Photographer: Daniel Acker/Bloomberg via Getty Images Up Next See Gallery Discover More Like This HIDE CAPTION SHOW CAPTION of SEE ALL BACK TO SLIDE

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