"I think it's up to Mitch McConnell and everyone else to stop it. It's called delay, delay, delay," he said.
Other candidates at the debate said that Obama should not nominate a new justice, praised Scalia's service on the court and urged a conservative replacement.
"Barack Obama will not have a consensus pick," said former Florida governor Jeb Bush.
"I just wish we hadn't run so fast into politics," said Ohio Gov. John Kasich.
Texas Sen. Ted Cruz said: "The Senate needs to stand strong."
Scalia, who was beloved by conservatives, died hours before the debate began. His death and the subject of who will replace him immediately become major topics of conversation in the debate and in the broader campaign. After the candidates took the stage, debate moderator John Dickerson called for a moment of silence for Scalia.
Also looming over Saturday's debate: Trump, the South Carolina front-runner who has come under a torrent of attacks from his rivals.
After skipping the final debate in Iowa and playing a secondary role in New Hampshire's last debate, Trump was positioned to be at the epicenter of Saturday's night's set-to in Greenville, South Carolina. He is fresh off a win in New Hampshire and is leaving the rest of the field in his dust, South Carolina polls show. And in the past 48 hours, his opponents have savaged him.
Adding to the testy atmosphere Saturday, Trump issued a statement accusing the Republican National Committee of "illegally" putting out a fundraising notice using his name before withdrawing it "at my insistence." An RNC aide said the notice Trump was citing was related to a straw poll where participants were asked to donate once they picked a candidate.
"The straw poll allows supporters of all the candidates to help contribute to the presidential trust that ensures our nominee has the $23 million of RNC funds to take on Hillary Clinton or Bernie Sanders," said RNC chief strategist and communications director Sean Spicer.
Saturday's debate was expected to test whether Rubio, who was ridiculed for mechanically repeating himself in the previous meeting, can regain his footing after a fifth-place finish in New Hampshire.
Several one-on-one competitions were expected to escalate on stage, because fewer candidates is likely to mean more talking time for each one. Among them: Trump vs. Cruz Rubio vs. Cruz, Rubio vs. Bush, and Bush vs. Kasich.
The two-hour clash, which CBS News is hosting, started at 9 p.m. Eastern time. This is the last debate before the Feb. 20 South Carolina primary.
Trump once again stood at the middle of the stage. He held a commanding lead in South Carolina, home to nearly 5 million people, including an eclectic mix of Republicans. There are many Christian conservatives, defense hawks and centrists in the state.
Trump released an ad this week focusing on his signature issue: immigration. The father of an African American teenager killed by an illegal immigrant explains why he supports Trump in the ad.
"Trump is the only one saying: You're going to be dealt with. We're going to enforce that," Jamiel Shaw says in the ad. "We're going to enforce that. That's a beautiful thing."
Trump has voiced hard-line positions on immigration, including banning all Muslims from entering the country over concerns about terrorism and creating a "deportation force" to remove undocumented immigrants.
But in genteel South Carolina, Trump's challengers have taken aim at his brashness as much as they've targeted his policy ideas.
On the campaign trail this week, Rubio has criticized Trump for using crude language that he said he had to shield from his young sons. Right to Rise USA, a super PAC promoting Bush released an ad Friday calling Bush "the better man" and highlighting Trump's personal attacks.
Rubio is trying to reignite a campaign that fell apart in the final days before the New Hampshire vote. He is showing a personal side he hopes will wipe away accusations that he is too robotic. He also has adopted a more aggressive posture, hitting not just Trump but Bush, whom he argues does not have any foreign policy experience.
Bush, who finished just ahead of Rubio in New Hampshire, is trying to edge ahead of the senator in the battle for the mainstream Republican mantle. A strong showing in South Carolina, where Bush's father and brother won primaries, could deal a devastating blow to Rubio.
On Monday, former president George W. Bush plans to campaign with his brother at a rally in North Charleston, South Carolina, after mostly staying out of politics since he left the White House in 2009.
Rubio is not the only opponent Bush needs to worry about. Kasich, who finished a strong second in New Hampshire, has secured new financial support in recent days. He threatens to pull away some centrist Republicans also drawn to Bush.
Another battle that was raging heading into Saturday was the one between Trump and Cruz. Cruz's campaign released a video this week that says Trump "pretends to be a Republican." On Friday, Trump tweeted: "If @TedCruz doesn't clean up his act, stop cheating, & doing negative ads, I have standing to sue him for not being a natural born citizen."
Also on the stage is retired neurosurgeon Ben Carson, who has faded sharply after exploding onto the national political landscape last year. Carson is polling at the bottom of the field in South Carolina.
At the start of the race, the field was so crowded that organizers opted to hold two debates: a so-called undercard showdown for lower-performing candidates and a mainbar forum for the leading contenders. It continued that practice for months.
The field narrowed considerably after the first two nominating contests. This week, New Jersey Gov. Chris Christie, former Hewlett-Packard chief executive Carly Fiorina and former Virginia governor Jim Gilmore ended their campaigns.
After the South Carolina primary, the race will quickly move west to Nevada, which will hold its Republican caucuses three days later.
© 2016 The Washington Post
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.