Benjamin Netanyahu warned Theresa May that Iran “seeks to annihilate Israel” and “threatens the world” as the pair met for the first time for talks at Downing Street.
The two prime ministers also discussed bilateral trade and Middle East peace during a “working lunch” on Monday.
In opening remarks Theresa May said she was willing to discuss Iran – but Downing Street later stressed the "nuclear deal is vital and must be properly enforced and policed."
Downing Street also later confirmed the pair had established a new UK-Israel Trade Working Group "to prepare the ground for a post-Brexit trade agreement."
Mrs May also reiterated Britain’s call for a two-state solution and said the UK was a “strong and close friend of Israel” as she highlighted their co-operation in science, trade and security.
The meeting had got off to a faltering start after Mr Netanyahu was left waiting for Theresa May to meet him outside the door of No10 after a mix-up by both camps botched a planned photograph outside the famous black door.
Downing Street sources confirmed that PM May had planned to pose with the Israeli PM outside No10 - but his early arrival on Monday morning meant Mr Netanyahu was left standing outside Downing Street for around 15 seconds before entering the building alone.
In an attempt to remedy the PR glitch, the pair emerged together two minutes later to shake hands in front of the media.
Once the meeting began the Israeli PM 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 (US) 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.”
Highlighting Britain’s strong links with Israel in trade, security and science, Mrs May added:” there was “much more we can do” and that it was important to look at how “we can build that relationship”.
“But also talking about some issues around the region, Syria and Iran and the whole question of the future of the Middle East,” she added.
“And certainly we remain committed to a two-state solution as the best way of brokering stability and peace.”
The meeting was greeted by a demonstration by the Palestine Solidarity Campaign and a counter-demo organisational by the Zionist Federation.
Around 200 protesters from the PSC – one who carried a banner declaring ‘Jerusalem Is Ours’ – and around 150 from the ZF demonstrated in Whitehall, across the road from the meeting between the two leaders.
A large police presence ensured the protests went ahead without incident.
As the meeting took place, Jeremy Corbyn, Labour leader, urged Mrs May to tell Mr Netanyahu that continued settlement building “undermines trust”.
Mr Corbyn said: “That is simply not good enough. The Israeli government’s decision to build 3,000 new settlement homes in the occupied West Bank and East Jerusalem is illegal under international law and a threat to peace and international security.
“It further undermines the prospect of a two-state solution to the Israel-Palestine conflict, about which the Netanyahu government is increasingly contemptuous.”
Mr Corbyn, a long-standing supporter of the Palestinian cause, said the British government must “stand unequivocally behind the rights of the Palestinian people”.
In a reference to the row over an Israeli embassy employee’s comments about Foreign Office minister Sir Alan Duncan last month, Mr Corbyn said Mrs May should “demand an assurance” from her Israeli counterpart that “improper interference in British democratic politics” will not be repeated.
A large protest against Mr Netanyahu’s visit took place in Whitehall as the prime ministers met in Downing Street.
Activists from the anti-Israel Palestine Solidarity Campaign chanted for “Palestine to be free, from the river to the sea”, while a counter-protest led by pro-Israel groups also took place.
Leaders from the Zionist Federation, Board of Deputies and other groups waved Israeli flags as Mr Netanyahu arrived at Number Ten.
After meeting Mrs May, the Israeli prime minister held talks with Boris Johnson, the Foreign Secretary.
In a photo posted on Twitter, the pair were shown sitting beside the desk on which the Balfour Declaration was written in 1917.
Speaking in the Commons shortly after the two leaders met at Number 10 for their first bilateral meeting, Ms May made no mention of further sanctions against Tehran.
A Downing Street statement later said:"On Iran, the Prime Minister was clear that the nuclear deal is vital and must be properly enforced and policied, while recognising concerns about Iran's pattern of destabilising activity in the region."
Number 10 also confirmed the two leaders had discussed trade, security, technology, defence and security.
Mrs May invited PM Netanyahu to attend Balfour Declaration events in the UK to mark the 100 year anniversary of the signing in November as a guest of government.
Mrs May was also offered an invitation to visit him in Israel - while Lord Price will "visit Israel soon" to take the UK-Israel Trade Working Group forward.