President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE predicted he and North Korean leader Kim Jong Un will have a “terrific relationship” as the two leaders started their historic summit in Singapore on Tuesday.

“I feel really great,” Trump told reporters. “We’re going to have a great discussion and I think tremendous success. We’re going to be tremendously successful, and it’s my honor, and we will have a terrific relationship.”

Trump made the comments sitting next to Kim minutes after the two leaders shook hands for the first time, images that were broadcast worldwide.

Trump's one-on-one meeting with Kim kicks off the first-ever summit between a sitting U.S. president and a North Korean leader.

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After the greeting at the Capella resort on Singapore’s Sentosa Island, the two leaders walked to a room at the hotel and sat with American and North Korean flags behind each of their chairs.

Trump and Kim are scheduled to talk to each other alone for about 45 minutes with only their translators in the room before their advisers join them.

After Trump's comments, Kim, speaking through a translator, said the meeting showed the United States and North Korea have overcome past obstacles.

“The old prejudices and practices worked as obstacles on our way forward, but we’ve overcome all of them, and we are here today,” he said.

Trump then extended his hand for another handshake, after which Trump gave a thumbs-up.

Despite the optimism, it’s unclear whether the gap between the United States and North Korea over what denuclearization means has been bridged.

Trump has in the past week described the meeting as the first in a process and meant for the two leaders to get to know each other.

Trump tweeted hours before the meeting that “we will all know soon” whether he can broker a deal with Kim that would help stave off the threat of nuclear war.

“Meetings between staffs and representatives are going well and quickly ... but in the end, that doesn’t matter,” he tweeted. "We will all know soon whether or not a real deal, unlike those of the past, can happen!”