He spoke out while accompanying Mrs May on her three-day trade mission to China, suggesting moaning Tories should look at her efforts to promote British interests overseas.
His remarks follow growing criticism of the Prime Minister from a string of Tory MPs and donors, with some attempting to persuade her to set a timetable for her departure from Downing Street.
Asked whether Mrs May would lead the party into the next election due in 2022, Dr Fox said: “I will give full support to the Prime Minister as long as she wants to lead my party.
“I think she is doing an excellent job and I do wish more of my colleagues could see the sort of leadership and commitment and positive agenda that’s been projected for Britain here in China.”
He added: “When I’ve been talking to Chinese leaders, the Theresa May they see is the Prime Minister of a country with record employment, the highest number of people ever employed in our country, with more foreign direct investment coming into our country than ever before that’s seen 58,000 tech start ups in Britain in the last year, that’s seen our exports rise by 16% in goods and 11% in services in the past year.
“They [the Chinese] are looking at performance, they are looking to see what the UK is doing and they look at the Prime Minister in a different way than some of lets say the internal tea room discussions in the UK do and I sometimes wish that first of all people could see the Prime Minister the way that she’s seen in other countries in terms of the vision that she’s put forward for Britain and secondly I wish they could see Britain in the way that the rest of the world sees us and not the some of the internal commentators in the UK.”
Dr Fox also suggested many MPs should make a great effort to think globally rather than just focusing on Britain’s internal affairs.
“I think that in Britain there’s always a tendency to focus on Britain, inside Europe there’s a tendency to focus on Europe – both should be focusing on the big world that’s outside.
“Here we are in China – by 2030 China will 220 cities of more than a million people.
“The whole of Europe will have 35.
“Where should we be focusing our attention?” he said.