The Sunni Gulf monarchies and Tehran are at odds over a range of issues including the wars in Syria and Yemen
Iran's alleged "interference" in the region is a central preoccupation of the six-nation Gulf Cooperation Council whose most powerful member is Saudi Arabia.
The Sunni Gulf monarchies and Tehran are at odds over a range of issues including the wars in Syria and Yemen.
"We must... continue to confront state actors whose influence fuels instability in the region," May told Gulf leaders at their annual summit.
"So I want to assure you that I am clear-eyed about the threat that Iran poses to the Gulf and to the wider Middle East."
She added: "We must... work together to push back against Iran's aggressive regional actions."
May said she wanted a "strategic partnership" to help boost security in Gulf countries, including defence investment and military training in Bahrain and Jordan.
The prime minister also spoke about discussions to improve trade ties with Gulf countries as Britain prepares to leave the European Union after a shock referendum vote in June to quit the bloc.
"I want these talks to pave the way for an ambitious trade arrangement" after Brexit, she said in Bahrain, which was a British protectorate for 100 years and gained full independence in 1971.
May is the latest foreign leader to address the GCC as the Gulf deepens ties with major powers beyond longtime ally the United States.
Britain, too, is seeking "stronger global ties" before Brexit, finance minister Philip Hammond said on Wednesday.
In May last year, France's President Francois Hollande became the first Western head of state to attend a GCC summit since the bloc's creation in 1981.
US President Barack Obama in April also joined a GCC summit in Riyadh, seeking to reassure Gulf monarchs about US overtures to Iran.
GCC leaders have expressed concern over an international agreement that lifted sanctions on Iran this year in exchange for guarantees it would not pursue a nuclear weapons capability.
Riyadh and its allies fear the pact will lead to more Iranian intervention in a region which, Gulf leaders feel, has suffered from a lack of American involvement under Obama.
King Salman of Saudi Arabia opened the summit on Tuesday with a call for a "doubling of efforts" to face regional challenges.
In October last year, Britain began building a naval base at Mina Salman, outside Manama, its first new permanent base in the Middle East in four decades.
The EU including Britain is the Gulf's biggest trading partner, with trade flows of more than 130 billion euros ($140 billion) annually.
But almost 30 years after the Gulf states and the European Union began talks on free trade, still no deal has been reached.