The US President’s words come after Kim Jong Un visited China in his first foreign trip since taking power.
Mr Kim met the Chinese President Xi Jinping ahead of planned summits between North Korea, South Korea and the US, with the three having agreed to talk to allay tensions over Mr Kim’s nuclear ambitions.
Mr Trump wrote on Twitter: “Received message last night from Xi Jinping of China that his meeting with Kim Jong Un went very well and that Kim looks forward to his meeting with me.
“In the meantime, and unfortunately, maximum sanctions and pressure must be maintained at all cost!”
The three-day visit by Mr Kim to China was confirmed on Wednesday only after he had returned to North Korea.
Mr Kim and Mr Xi had held talks at Beijing’s Great Hall and Mr Kim had promised he was “committed to denuclearisation”, according to China’s Xinhua news agency.
Earlier Mr Trump had written that there was a “good chance” the secretive North Korean regime would move towards peace.
He said: “For years and through many administrations, everyone said that peace and the denuclearisation of the Korean Peninsula was not even a small possibility.
“Now there is a good chance that Kim Jong Un will do what is right for his people and for humanity.
“Look forward to our meeting!”
Mr Trump has agreed to meet Mr Kim by May, with speculation that the historic summit could take place in Sweden.
The agreement came after a surprise about-turn by Mr Kim, who offered to meet the US leader.
Mr Trump, who has previously traded insults with him, accepted the offer, hailing it as “great progress”.
North Korea has continued to pursue its nuclear programme and missile tests over recent years, ignoring international condemnation.
It has promised to stop these while talking with the US, however.