As authorities search for accomplices in the attacks, France launched airstrikes against the ISIS base in Raqqa on Sunday night in retaliation for the suicide attacks that killed at least 129 people.
Since 2013, Raqqa has been bombed extensively by the United States, France, Russia and various Arab states, including Syria itself.
The U.S. and its allies should have also been hitting the terrorist funding streams on the oil and banking fronts, Trump told CNBC's "Squawk Box" in a phone interview Monday.
"I've been saying attack the oil for two years. People would laugh, and they'd scoff, and they'd joke," he said. "Now all of a sudden, they started attacking the oil because that's a significant source of their wealth."
He lashed out at President Barack Obama for what he said was a weak and ineffective response to terrorism. He said Obama won't even use the term "radical Islamic terrorism."
"This is a war. They don't wear uniforms," Trump said, adding the "cancer" of terrorism needs to be stopped before it "festers and festers and only gets worse."
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Trump also blamed Democratic presidential front-runner Hillary Clinton for contributing to the problems in the Middle East when she was Obama's secretary of state.
"She's not the right person for this job," he said. "I would love to run against her."
Obama on Sunday met with Russian leader Vladimir Putin on the sidelines of the G-20 meeting in Turkey to discuss the situation in Syria. Russia has been bombing Syrian rebels fighting President Bashar Assad, including ISIS. In a speech Monday at the G-20 meeting in Turkey, Obama reaffirmed those plans, saying that not accepting refugees in the wake of the attacks would betray U.S. values.
Trump said he would "love the idea" of the U.S. and Russia working together to root out the Islamic State.
But while the U.S. and Russia have a mutual interest against ISIS, the two countries differ on whether Assad should stay in power. Russia wants him to stay. The U.S. wants him to go.
"The problem is, we want to get rid of Assad, but we don't know who we're getting rid of," Trump said. "It's not like we have 'George Washington' that we're backing. We're backing people who we have no idea who they are."
Pointing to other flashpoints, including Libya and Iraq, where dictators were deposed, Trump said in many cases the situations in those countries have gotten worse.
The Paris attacks have also raised new questions about how to deal with the Syrian migrant crisis in Europe, while two American states, Alabama and Michigan, said they will not allow the resettlement of Syrian refugees in those states.
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"You can't let them in" the U.S., Trump said. "When I look at that migration, I see a lot of very strong, young men. And I see far fewer women and children. I say, ''What's going on over here?'"
"It would be one of the great Trojan horses," he said.
Obama plans to allow as many as 10,000 Syrian refugees come to the U.S., a plan that an administration official said Sunday would still move forward.
Trump said such a plan would enable him to win the White House, and if so, he would expel the migrants.
On Sunday, Republican contender Marco Rubio said on ABC's "This Week" the U.S. should not admit the refugees because it's impossible to know whether those fleeing Syria have links to Islamic militants.
Former Florida Gov. Jeb Bush told NBC's "Meet the Press" on Sunday the U.S. should admit Syrian Christians, after proper vetting. Other Republican candidates have called for a ban altogether.
Separately, all three Democratic presidential candidates have said they would admit Syrian refugees, but only after thorough background checks.
— Wire services contributed to this report.