Republican U.S. presidential candidate Donald Trump said Sunday the only way to defeat the Islamic State group is to take away its source of wealth. In remarks on CNN's "State of the Union," Trump praised Russia for going after the militant group formerly known as either ISIL or ISIS.

"We've got to hit ISIS hard," Trump said, without getting into specifics. However, he did say he would "knock out their source of wealth ... take the oil away."

Trump made the rounds of Sunday-morning television talk shows by phone.

Trump told ABC News' "This Week" he welcomes the Russian decision to bomb Islamic State group targets in Syria, but he's still not convinced the militant group was responsible for downing the Russian passenger plane that crashed in Egypt's Sinai Peninsula Oct. 31.

"We can't be sure it was ISIS, [but if it was] we're going to have to do something strong over there," Trump said. "We have to stop the source of money, and the source of money is the oil. ... ISIS is making a fortune."

metrojet Debris of a Russian Airbus A321 lies on the ground Nov. 1, 2015, a day after the plane crashed in Wadi al-Zolomat, a mountainous area in Egypt’s Sinai Peninsula. Photo: Khaled Desouki/AFP/Getty Images

Trump's appearances came just hours after the real-estate mogul hosted NBC's "Saturday Night Live" and poked fun at his campaign-trail persona, acknowledging he has been short on specifics on most issues. "I don't have to get specific," Trump said in one sketch. "It's just magic."

Trump promised on CBS News' "Face the Nation" to unveil his proposed federal budget cuts soon. He indicated he planned to plug loopholes that make tax havens attractive and eliminate the carried-interest deduction used by hedge-fund managers, but promised not to eliminate the home-mortgage deduction.

His CNN interview touched on other issues, including immigration. Trump has urged construction of a wall along the U.S.-Mexico border and promoted the deportation of undocumented immigrants. "We have to do what [President Dwight D.] Eisenhower did in the 1950s," Trump said, referring to "Operation Wetback," an effort coordinated with Mexico that saw the deportation of more than 1 million people in its first year of operation.

On NBC News' "Meet the Press," Trump said he'd use the trade imbalance between the two countries to get Mexico to pay for a wall on the border. "We can build a magnificent wall, and when you have a trade imbalance ... it's really easy to negotiate that deal," he said.

Trump insisted he had put out details on his positions, citing his tax plan and programs for military veterans. He also said he is the only one of the presidential candidates who knows how to negotiate a deal and would put his negotiating skills to good use, should he be elected.

About his "SNL" appearance, Trump said comedian Larry David's heckling was in the script. Toward the end of the candidate/host's monologue, David appeared to have take to heart Deport Racism's offer of $5,000 to anybody who yelled, "Trump's a racist," during the show. "It was part of the script," Trump said.

Trump took backhanded stabs at retired neurosurgeon Ben Carson, who has bested him in some recent opinion polls. Trump said repeatedly in each of his appearances that he likes Carson and feels for his rival now that media scrutiny on him has intensified. In recent days, various media have cast doubt on statements Carson has made about his propensity for violence as a teenager and whether he had won a scholarship to the military academy at West Point.

"It's a tough thing," Trump said on "Meet the Press." "He's going to have to explain a lot of things away." Trump indicated he thinks Carson has been less than truthful.

On "Face the Nation," Trump said he hopes it "all works out" for Carson. "I don't know what he's doing. ... It's a lot of statements that are very troubling statements."