Theresa May has said the UK was a "close friend of Israel" as she met Israeli Prime Minister Benjamin Netanyahu for the first time.
The Prime Minster highlighted their joint co-operation in science, trade and technology and said there was "much more we can do" to deepen ties.
In her opening remarks, she said it was important to look at how "we can build that relationship".
She added: "But also talking about some issues around the region, Syria and Iran and the whole question of the future of the Middle East.
"And certainly we remain committed to a two-state solution as the best way of brokering stability and peace."
Mrs May's first meeting with Mr Netanyahu got off to an awkward start after he arrived two minutes early and was left standing outside the famous black door of Number 10.
The Prime Minister did not greet her Israeli counterpart and he was left to enter alone, 15 seconds later.
However they emerged two minutes later and shook hands in front of the assembled media.
Downing Street sources said a mix-up inside Number 10 meant the photo opportunity did not go according to plan.
Downing Street had hoped the meeting would focus on bilateral issues, especially trading opportunities, once Britain leaves the European Union.
However Mr Netanyahu is likely instead to press ahead with forming a "common front" against Iran - days after Tehran test-fired a ballistic missile - which could test her diplomacy.
Britain was one of the signatories to the 2015 international agreement aimed at curbing Iran's nuclear programme in exchange for the lifting of economic sanctions.
Mr Netanyahu has said the bad deal will do nothing to halt Iran's nuclear ambitions.
Their talks are also likely to involve Israeli settlements in the West Bank.
Most of the international community have viewed the settlements as illegal and a hindrance to the two-state solution.
Mrs May is under pressure to condemn the building on occupied Palestinian land and will raise Britain's concerns during the meeting.