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.
Grant Shapps, a former Conservative Party chairman, was among MPs to air the party's disquiet over May's leadership, even comparing her to Margaret Thatcher.
She said: "I'm in this for the long term".
May called a snap general election in June, hoping to extend the centre-right Conservatives' slim majority and strengthen her hand going into the Brexit negotiations.
"It is my intention not just to deliver a good Brexit deal for the United Kingdom but also to ensure that "global Britain" can take its place in the world, trading around the world and that we deal with those injustices domestically that we need to do to ensure that stronger, more global but also fairer Britain for the future". "But we also need to ensure that, after we have left the European Union, global Britain is out there trading around the world, standing tall in the world and that we deal with some of the remaining injustices at home".
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.
"The truth is we ran a very poor election and you can't just brush that under the table and pretend it didn't happen - not least because we went from having a workable majority to no majority at all, so that stands to reason", he told BBC Radio 4's Today programme.
"I'm not a quitter", May said in an interview with ITV News during a visit to Japan.
One unnamed Tory former minister said Mrs May may have ended up "hastening her own demise", while a senior MP said they were "utterly dismayed" by the remarks. "Let's get some progress for the British people first; I think that's the priority".
The London Evening Standard, now edited by George Osborne, the Conservative sacked by May as finance minister when she became prime minister past year, described her pledge to run again as "Like the Living Dead in a second-rate horror film".
"Whilst Theresa May is desperately trying to spin this visit as scoping out a future bilateral trade and investment agreement, the reality is that the government is spooked by the fact that Japanese banks like Nomura have already announced their intention to relocate", he said.
"We have the right leader and PM to deliver this for us".