Theresa May will discuss her hopes for post-Brexit trade deals with the United States and Japan on the final day of the G20 summit.
The Prime Minister will also tell leaders Donald Trump and Shinzo Abe that Britain stands with them in the battle to quash the "growing threat" from North Korea following its increased programme of nuclear weapons testing.
Mrs May is holding early morning talks with Mr Trump in the margins of the gathering of world leaders in Hamburg, Germany.
As well as discussions on a possible future trading agreement with the US when Britain leaves the European Union, Mrs May will raise the president's controversial decision to pull out of the international agreement on tackling climate change.
Mrs May said she hopes Mr Trump will take the US back into the Paris Agreement.
She told ITV News: "I will be making that message. I will continue to give the message that the United Kingdom believes in the importance of the Paris Agreement".
In a meeting with Mr Abe on Saturday afternoon the Prime Minister will talk about trade and also offer Japan British help on counter-terrorism and cyber security when it hosts the rugby world cup in 2019 followed by the Olympics.
Mrs May is also holding one-to-one talks with Turkish president Recep Tayyip Erdogan to discuss ways to tackle the increasing numbers of Islamic State fighters leaving Syria across its border.
It comes after the first day of the summit saw Mr Trump hold talks with Russian president Vladimir Putin, which Moscow described as "very constructive".
Newly elected French president Emmanuel Macron had earlier made his frustrations with his US counterpart clear in a private meeting of all the leaders when he hit out at Mr Trump's America first trade policy.