"I welcome the fact that the United Nations Security Council has been united in its condemnation of the actions of North Korea".
Her comments come after a North Korean missile was sacked over north Japan, before crashing into the sea.
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.
The source added the leaders wanted to increase the effectiveness of the current sanctions by helping others to implement them.More news: The iPhone 8's dock might work more like the new iPad's
She and Japanese Defense Minister Itsunori Onodera met on the Izumo at a naval base in Yokosuka, south of Tokyo.
British Prime Minister Theresa May called on China to put more pressure on North Korea to stop missile tests, saying Beijing has a key role to play in worldwide efforts to prevent what she described as significant provocation by Pyongyang. "We must work together to enhance our collective response to the threats to the worldwide order and global peace and security", she said.
Number 10 said the Prime Minister and her Japanese counterpart Shinzo Abe will "explore" fresh sanctions against Kim Jong Un's regime in a second day of talks on Thursday.
"So I am determined that we will seize the opportunity to become an ever more outward-looking global Britain, deepening our trade relations with old friends and new allies around the world", she said, according to Britain's Press Association.More news: Samsung announces Gear Fit2 Pro, Gear Sport
May described Japan as "the UK's closest security partner in Asia" and a "like-minded partner".
May is visiting Japan for the first time as prime minister.
Fox said his country will continue working to attract Japanese investment.
"And by the visit today it gives a sign of the growing cooperation and partnership that we have on defence". She is to meet Emperor Akihito on Friday before leaving.More news: Nigeria Confirms Its 5 Pilgrims To Mecca Have Died
The US and Japan also plan to call for an worldwide ban on oil exports to North Korea in a United Nations Security Council emergency meeting next Tuesday, Japan's Nikkei Asian Review reported.
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