"As we meet today, North Korea continues to take provocative action in the Asia-Pacific region," May said during a joint news conference.
"In the face of this belligerence we stand steadfast in our condemnation of such destabilising activity," she said.
The visit, Abe's first since May took office in July 2016 after the Brexit vote, comes as the UN Security Council gathers in New York to discuss the situation in North Korea.
Condemning North Korea's nuclear and missile tests as a "violation of United Nations Security Council resolutions and international obligations", May vowed to continue to "maintain pressure on North Korea".
The two leaders also agreed to "stand firm in the face of destabilising Russian activity" in Ukraine and Syria through the use of sanctions.
Abe's visit to the UK follows a visit to Russia on Thursday where he met President Vladimir Putin for talks on a decades-old territorial dispute over an island chain.
The Soviet Union seized the islands off Japan's northern coast -- called the Southern Kurils by Moscow and the Northern Territories by Tokyo -- in 1945 in the closing days of World War II.
Abe and Putin also sought to boost trade and economic ties hit by Japan joining sanctions on Russia over the crisis in Ukraine.
Meanwhile, the British prime minister sought to secure investment and trade with Japan, the fourth-biggest source of foreign direct into the UK, according to statistics agency ONS.
"The UK remains the best place to in Europe to run and grow a business," she said.
Abe was quite critical of Brexit ahead of the June 2016 referendum, saying during his last visit to the UK a month before the vote that Britain would become "less attractive" for Japanese companies if it chose to exit the bloc.
But on Friday, Abe told May that he continues "to have confidence in the economy of the UK".
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