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Speaking to a US television program Sunday about the North Korea issue, Trump said he was happy to "sit down with anybody."
"I would sit with anybody I feel. I don't think it's strength or weakness. I think sitting down with people is not a bad thing," he said.
"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," Trump tweeted, adding "we'll do what has to be done!"
Asia trip
"We want Putin's help on North Korea, and we'll be meeting with a lot of different leaders," Trump told reporters aboard Air Force One en route to Japan.
Before Trump sees Putin in the Vietnamese seaside city of Da Nang, he will have visited three Asian capitals on his North Korea diplomacy mission. After talks here with Japanese Prime Minister Shinzo Abe, Trump will head to Seoul and Beijing for state visits that are also set to include discussions of trade and security.
That trip may coincide with the US designating North Korea a state sponsor of terror. A senior administration official said that decision will be made "very soon."
"The administration and Secretary (of State Rex) Tillerson and others in the administration are looking very closely right now whether to designate North Korea a state sponsor of terror," the official said Sunday. "I would expect an answer very quickly."
When asked whether that meant an announcement would come during Trump's trip, the official only said: "Stay tuned."
CNN's Kevin Liptak contributed reporting.