Yasutoshi Nishimura, Japan's deputy chief cabinet secretary, said Brexit had created a "sense of crisis among businesses" and the country's prime minister, Shinzo Abe, would be seeking May's reassurances.
Meanwhile, Grant Shapps, the former Tory party chairman, said Mrs May could not "jump straight" from throwing away the Tories' majority to announcing an intention to remain as leader well into the next decade as he signalled she would have to prove herself. "The long term is the hard one for Theresa May because I don't think she's got a long term", he said.
In a series of interviews, Mrs May promised to deliver social reforms aimed at a "brighter future".
"As our closest security partner in Asia, we will also discuss how we can work much more closely together on cybersecurity, counter-terrorism and defence - more important than ever in this uncertain world", May said.
The next national election is not scheduled until 2022, three years after Britain is due to leave the European Union.
Her hold on the leadership has been fragile since her decision to hold a snap general election which resulted in the Conservatives losing their Commons majority. Prior to May's visit, Japanese officials said there would not be "substantial progress" on a trade deal until the UK's future relationship with the European Union was clarified, dashing May's hopes, the Financial Times reports.
She set down the marker after a summer of speculation about her leadership, and mischief-making including suggestions that colourful backbencher Jacob Rees-Mogg is ideally placed to take the helm.
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One MP has told the FT that the prime minister appears to be "harbouring delusions" and that she can not win a general election.
Ms Morgan told BBC's Hardtalk that no leader wants to put a date on their departure in advance because it is a sign of "your own political mortality". "Let's get some progress for the British people first, I think that's the priority", he told BBC Radio 4's Today program.
Asked during a visit to Japan whether she wanted to lead the Conservative Party into the next election, May said: "Yes".
Senior Tories have indicated that Theresa May will not be supported in her ambitions to run for a second term as Prime Minister.
She added: "I think for most members of the public they would say they want the government to get on with the job and that's exactly what I and the government are doing".
Japan said last September it was concerned about the repercussions of Brexit on its investment in and trade with the United Kingdom, though the vehicle company Nissan has since committed to staying in the UK.