Mrs May earlier called on China to step up its action against North Korea and refused to rule out Britain getting involved in military action to stop the rogue state's illegal weapons programme.
"North Korea's recent ballistic missile launch on August 29, which passed over Japan, was an outrageous provocation and posed an unprecedented, serious and grave threat to Japan's national security", the joint statement read.
When asked to elaborate, May said there were "a number of issues that China can look at", such as further worldwide sanctions against Kim Jong Un's regime. North Korea threatened "thousands-fold" revenge on the USA after these sanctions were announced.
"But also going out around the world ensuring that we can do those trade deals that bring prosperity to our economy and bring jobs to the United Kingdom".
Kushner leads U.S. delegation for peace talks in Middle East
Saeb Erekat, Presidential Advisor for Economic Affairs Mohammed Mustafa, head of the General Intelligence Service Maj. The report of the planned USA proposal came amid recent signs of disillusionment from Abbas over U.S. peace efforts.
"In response to this illegal action, Prime Minister (Shinzo) Abe and I had agreed to work together and with others in the global community to strengthen pressure against North Korea including by increasing the pace of sanctions".
However, a Chinese foreign ministry spokesman said the focus should be on de-escalating tensions not "just chanting about sanctions". On Tuesday, it fired a missile over Japanese territory.
Downing Street said the length of time the PM had spent with Mr Abe on the first day of three-day visit was "unusual" and demonstrated the "strength and continuing positive relationship" between the two.
"We absolutely do not tolerate the nuclear and missile development by North Korea". But Japanese officials on Tuesday shot down the UK's hopes for a quick trade agreement, saying said they were in no rush to enter negotiations with Britain, especially since it is now negotiating a free trade agreement with the EU.