She said she would ask him to push ahead with a wide-ranging EU-Japan trade deal, with the idea it could then be used as a model for a separate deal with the UK.
"Prime Minister Abe and I have agreed to work together, and with others in the worldwide community, to strengthen pressure against North Korea, including by increasing the pace of sanctions implementation", May told a joint news conference with Prime Minister Shinzo Abe on Thursday.
Shinichi Iida, an official at the Japan's London embassy, said Japanese businesses had a "big stake" in the Brexit process but needed reassurance.
William Hague has blamed the British public for making "a mistake" at the general election, by failing to return a Conservative majority and weakening the country's hands in the Brexit negotiations with the EU.
Foreign Secretary Boris Johnson, viewed as a potential candidate in any future Tory leadership contest, said the Prime Minister had his "undivided" support but former cabinet minister Nicky Morgan said it would be "difficult" for Mrs May to lead the party into the next election, due in 2022.
But some lawmakers have come out to defend the Prime Minister.
Lord Hague, who has previously warned that only a transition deal can save the United Kingdom from disaster, said the weak government returned by the electorate in June would mean the United Kingdom would end up paying more to leave the EU.
Downing Street hopes the trip will help fix May's dented authority, and show that Britain will retain close relations with major trading powers after Brexit.
It said the focus of talks with Japanese Prime Minister Shinzo Abe will be on defence and security cooperation, as well as trade and investment. On Friday she will have an audience with Emperor Akihito.
Taylor Swift serves as bridesmaid at best friends wedding
The 27-year old singer stunned fans when spotted at Martha's Vineyard, Massachusetts, accompanying her best friend on her special day.
High profile Tory MPs have told City A.M. they are minded not to rebel over the coming Brexit bill, with one saying the Prime Minister had scraped through sufficiently to suggest she could remain in the top job until 2019, characterising the next couple of years as "bumpy stability".
Among the business delegation will be executives from Barclays, the Scotch Whisky Association and Aston Martin.
Some 17% of Britons say Theresa May resigning would make them more likely to vote for the Tories, while nine percent say it would make them less likely to do so. "We think that if that's concluded swiftly it provides a good basis for continuity once we leave".
"Theresa May leads a zombie government".
With a nod to her trade discussions in Japan, Mrs May said:"But it's also about building global Britain, trading around the world".
But persuading Japan to agree to trade with Britain on the same terms as the European Union is a "lofty goal", Bloomberg writes.
"The most likely person hardly ever gets it".
North Korea fired a ballistic missile over Japan's northern Hokkaido island into the sea early on Tuesday, prompting warnings to residents to take cover and drawing a sharp reaction from Tokyo.