But Mr Johnson put those reservations aside to hold for meetings with Mr Trump's inner team including Steve Bannon, chief strategist, and Jared Kushner, the president-elect's son-in-law. There had been speculation he might meet Mr Trump himself, but the encounter never came to pass.
The talks covered foreign policy issues and will have helped prepare for Mrs May's visit to the White House, expected next month. On Monday Mr Johnson will meet Congressional leaders in Washington, including Speaker Paul Ryan, Senator Bob Corker and Senator Mitch McConnell.
Mrs May is expected to meet the new president in Washington next month and has gone out of her way to curry favour with the new administration, in spite of her concerns about Mr Trump's previous comments about women.
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To Mr Trump's observation brought up during the presidential campaign that being famous allowed a male star to molest women, Mrs May responded on Sunday: "I think that's unacceptable and in fact Donald Trump himself has said that."
Mrs May said she had "two very good, positive conversations" with Donald Trump. Her joint chiefs of staff met Mr Trump's transition team in New York last month to prepare her forthcoming visit.
Last month Downing Street criticized outgoing US secretary of state John Kerry after he made critical remarks about Israel's settlement-building program — Mr Trump is a strong supporter of Israel.