The two leaders spoke over phone yesterday during which May also briefed Trump on her recent trip to China, the White House said.
"The two leaders agreed all responsible nations must increase pressure on North Korea until it turns to the path of denuclearisation," the White House said.
"The leaders also agreed the pending United States-United Kingdom Data Sharing Agreement would benefit law enforcement efforts in both countries, and they will advocate for legislation together," the White House said.
"There are no plans to meet with any North Korean officials during or after the Olympics; I want to be clear about that. There are no plans to do so," State department Spokesperson Heather Nauert told reporters at her daily news conference.
North Korea last year increased the pace of its missile programme and launched 23 missiles since February.
In November, North Korean leader Kim Jong-Un said that his country had achieved full nuclear statehood after what he said was the successful test of a new missile capable of striking anywhere in the United States.