McConnell: North Korea summit beginning of an 'arduous process'
© Greg Nash

Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellTrump stays out of Arizona's ugly and costly GOP fight Sen. Warner to introduce amendment limiting Trump’s ability to revoke security clearances The Hill's 12:30 Report MORE (R-Ky.) said on Tuesday that the meeting between President TrumpDonald John TrumpWhite House counsel called Trump 'King Kong' behind his back: report Trump stays out of Arizona's ugly and costly GOP fight Trump claims he instructed White House counsel to cooperate with Mueller MORE and North Korean leader Kim Jong Un was a "historic first step" but warned there would be an "arduous process" before getting a nuclear agreement.

"Today is the beginning of the arduous process. Our eyes are wide open. I support the goals contained in the statement and I remain supportive of the administration's mission," McConnell said from the Senate floor.

McConnell's comments come after Trump and Kim signed an agreement committing the United States to unspecified “security guarantees” in exchange for a denuclearized Korean peninsula.

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McConnell added that the summit was a "historic first step" in talks between the two countries while stressing that there are still hurdles to getting an agreement that was palatable to both sides.

"The next steps in negotiations will test whether we can get to a verifiable deal which enhances our relationship with Northeast Asia and our allies. The challenge will take a great deal of hard work," McConnell said.

Republicans have been cautiously supportive of Trump's talks with Kim, while skeptical that the North Korean leader will ultimately agree to denuclearize.

McConnell, speaking at an event in Kentucky earlier this month, warned Trump against getting "snookered" in the talks.

"I think for these situations to work you have to not want the deal too much. If you fall in love with the deal and it's too important for you to get it ... you could get snookered. And I think the president's fully aware of that," McConnell said.