She also invited Mr Netanyahu to attend centenary celebrations of British support for a "national home" for Jewish people in Palestine announced by the then foreign secretary Arthur Balfour in 1917.
“As we prepare to mark 100 years since the Balfour Declaration, the Prime Minister underlined that Britain remains a close and firm friend of Israel and reiterated our support for Jewish communities in the UK.
"She invited Prime Minister Netanyahu to attend events taking place in the UK to mark the anniversary in November, as a Guest of Government. He also invited her to visit him in Israel.”
GETTY
Benjamin Netanyahu has urged Theresa May to take a tougher stance towards Iran
On a visit to Downing Street, Mr Netanyahu said "responsible" nations should follow US President Donald Trump's lead in imposing new sanctions on Tehran.
Ahead of their talks, he told Mrs May: "We face challenges, that's very clear, from militant Islam and especially from Iran.
"Iran seeks to annihilate Israel, it seeks to conquer the Middle East, it threatens Europe, it threatens the West, it threatens the world.
"And it offers provocation after provocation.
"That's why I welcome President Trump's assistance of new sanctions against Iran, I think other nations should follow suit, certainly responsible nations.
"And I'd like to talk to you about how we can ensure that Iran's aggression does not go unanswered."
GETTY
The Israeli PM claimed ‘responsible’ nations should impose new sanctions on Tehran
Mrs May signalled her willingness for further talks about how to respond to Iran while reaffirming her support for a deal that allowed the regime to develop nuclear power in return for forsaking a nuclear weapons programme.
We face challenges, that's very clear, from militant Islam and especially from Iran
Israeli prime minister Benjamin Netanyahu
Her spokeswoman said: "On Iran, the Prime Minister was clear that the nuclear deal is vital and must be properly enforced and policed, while recognising concerns about Iran’s pattern of destabilising activity in the region."
Mrs May and Mr Netanyahu also discussed building firmer trade links between Britain and Israel as the UK prepares to leave the EU.
“In their discussions, the Prime Ministers committed to working together to build on our longstanding relationship and the strong ties that already exist between our two countries in a wide range of areas, from trade and investment, to innovation and technology, and defence and security," the spokeswoman said.
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International trade minister Lord Price is to visit Israel soon to discuss trade between the UK and Israel, the spokeswoman said.
“They discussed their shared belief in free trade and agreed to establish a new UK-Israel Trade Working Group to continue the progress we have seen in our burgeoning trade and investment relationship, and to prepare the ground for a post-Brexit trade agreement.
"It was noted that Lord Price will visit Israel soon to take this forward.
"They also discussed opportunities to increase investment in research and development and technology, and strengthen partnerships in these areas between our governments, universities and businesses.
GETTY
Mr Netanyahu and Mrs May also talked about a trade agreement for after the UK leaves the EU
“They talked about the important work we do together on intelligence-sharing and cyber-security, and committed to talk further about how we can deepen this cooperation, to help keep our people safe."
Mrs May also indicated her desire to see progress in the Middle East Peace Process while raising concerns about Israeli settlements in Palestinian territory.
"They also talked about the Middle East Peace Process and the UK’s firm commitment to a two-state solution as the best way to bring stability and peace to the region.
"The Prime Minister reiterated the UK’s opposition to settlement activity."
GETTY
Mr Netanyahu invited Mrs May to visit him in Israel
She also invited Mr Netanyahu to attend centenary celebrations of British support for a "national home" for Jewish people in Palestine announced by the then foreign secretary Arthur Balfour in 1917.
“As we prepare to mark 100 years since the Balfour Declaration, the Prime Minister underlined that Britain remains a close and firm friend of Israel and reiterated our support for Jewish communities in the UK.
"She invited Prime Minister Netanyahu to attend events taking place in the UK to mark the anniversary in November, as a Guest of Government. He also invited her to visit him in Israel.”
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