Senate Majority Leader Mitch McConnell Melina Mara | The Washington Post | Getty Images

Top Republican lawmakers acknowledged Tuesday that the Trump administration has work to do to get North Korea to abandon its nuclear weapons, despite dictator Kim Jong Un's pledge to pursue "complete denuclearization." Notable GOP lawmakers applauded the summit in Singapore between Kim and President Donald Trump, calling it an important step toward peace in Asia. However, they warned that Pyongyang has proven reluctant to give up its nuclear ambitions in the past despite similar pledges. Republican lawmakers showed caution about North Korea's willingness to dismantle its nuclear weapons and suggested Trump still faces a long process to get a concrete commitment. Some experts told CNBC that Trump and Kim's agreement appeared vague and leaves possible sticking points between Washington and Pyongyang. Those potential disagreements include the definition of denuclearization.

Before departing Singapore, Trump repeatedly said he believes Kim will give up his nuclear and missile programs. The president thinks North Korean officials "want to make a deal" to get the international community to remove damaging economic sanctions. Still, Trump acknowledged he "may be wrong" about the prospects of a firm agreement, even if he may not admit it. Top Senate and House Democrats cheered the dialogue but worried Trump made concessions without getting firm commitments in return. They contended that Trump elevated the dictator's regime simply by meeting him, but did not move far enough toward a peace deal in the process.

Republicans want Trump to keep up "maximum pressure"

On Tuesday morning, Senate Majority Leader Mitch McConnell called the summit a "historic first step in an important negotiation." He stressed that ongoing talks "will test whether we can get to a verifiable deal which enhances the security of Northeast Asia, our allies and of course the United States." "If North Korea does not prove willing to follow through, we and our allies must be prepared to restore the policy of maximum pressure," the Kentucky Republican said on the Senate floor. "Maximum pressure" refers to the package of economic sanctions designed to get Pyongyang to give up its nuclear ambitions. Trump said Tuesday that sanctions will stay in place until "the menace of nuclear weapons" is removed. The president recently stopped using the maximum pressure term "because we're going into a friendly negotiation," he said Thursday. House Speaker Paul Ryan noted Tuesday that "we must always be clear that we are dealing with a brutal regime with a long history of deceit." In a statement, the Wisconsin Republican said "only time will tell if North Korea is serious this time." "The road ahead is a long one, but today there is hope that the president has put us on a path to lasting peace in the Korean Peninsula," he said.

House Speaker Paul Ryan (R-WI) Aaron P. Bernstein | Reuters

Several Republicans in the GOP-controlled Senate echoed McConnell in saying denuclearization is not a done deal. Multiple senators urged the Trump administration not to let up on economic sanctions amid ongoing talks. If Trump decides to structure the deal as a treaty, the Senate will have to approve it. Senate Foreign Relations Committee Chairman Bob Corker worried nothing significant came out of the summit. In a statement, the Tennessee Republican said, "It is difficult to determine what of concrete nature has occurred." Observers "should be skeptical of any deal" with Kim, Sen. Marco Rubio added. In a tweeted statement, the Florida Republican said he believes Pyongyang "will never give up nukes & [intercontinental ballistic missiles] unless they believe failure to do so triggers regime ending reaction." @marcorubio: Should be skeptical of any deal with #KJU Limits to future strategic weapons instead of eliminating current program not an acceptable outcome. Hope I'm wrong but still believe they will never give up nukes & ICBM's unless believe failure to do so triggers regime ending reaction The document Trump and Kim signed on Tuesday does not call for a change of leadership in North Korea. In a statement, Sen. Cory Gardner, R-Colo., said, "Today's summit must be followed by multiple meetings to test North Korea's promises of denuclearization, which they have made in the past and then repeatedly violated." Pyongyang has violated previous commitments in the 1990s and 2000s not to develop nuclear weapons.

Schumer sees 'great fear' Kim will not follow through

Senate Minority Leader Chuck Schumer (D-NY) Joshua Roberts | Reuters