On a visit to Japan, May also said Britain and the European Union must focus on their future relationship, "ensuring we can get that trade deal right and also that we can form new trade deals around the rest of the world". I think that they are significant actions of provocation.
Landing in Japan just 36 hours after Pyongyang sent a missile over the north of the country, the Prime Minister insisted the United Kingdom would be re-doubling its efforts to curb the regime's weapons testing programme.
Japan's Prime Minister Shinzo Abe called it an "unprecedented" threat to his country, while US President Donald Trump said it was an act of "contempt". She added: "We would encourage China to do everything it can".
Mrs May's trip to Japan is due to last for three days.
"We're never out of diplomatic solutions", he said, pointing to collaboration between United States and Seoul and saying the allies are "never complacent" when it comes to protecting their citizens.
Pyongyang has tested a barrage of missiles over the past years, but it is the first time it launches what is believed to be a ballistic missile over Japan.
Spokesman Park said the two leaders also agreed that the swift meeting of the UN Security Council (UNSC) and the adoption of a presidential statement was the result of close coordination between Seoul, Tokyo and Washington. May will lead a 15-strong business delegation, including Standard Life Investment chief executive Keith Skeoch, and carmaker Aston Martin's CEO Andy Palmer, pitching Britain and Japan as the "perfect partners for the future".She will meet Japanese Prime Minister Shinzo Abe in Kyoto before traveling to Tokyo for an investment conference and banquet.
Japan, which is negotiating a trade deal of its own with the European Union, has been forthright in expressing concerns about Brexit's impact on its UK-based firms, which employ about 140,000 people. "I think what Mr Abe wants to hear from the Prime Minister is where she hopes to land on Brexit".
Barry Gardiner, shadow secretary of state for global trade, said: "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 their European HQ to Frankfurt".