Theresa May is due to meet US President Donald Trump on the fringes of the G20 summit in Hamburg to discuss a post-Brexit trade deal.
The UK prime minister will also urge Mr Trump to reconsider his decision to take the US out of the Paris Agreement on climate change.
Earlier at the G20, Mrs May rejected claims that the UK was losing its global influence because of Brexit.
She insisted Britain would continue to be “bold” on the world stage.
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Mrs May said the UK remained a key international player in areas such free trade and counter-terrorism.
Amid speculation about her future after the election, she said she would take a lead, not “sit back” and be “timid”.
Mrs May said: “I will continue to give the message that the United Kingdom believes in the importance of the Paris Agreement.”
She will also meet Japanese Prime Minister Shinzo Abe on Saturday.
Their talks are expected to focus on trade, and she will offer Japan the UK’s help on counter-terrorism and cyber security for both the Rugby World Cup in 2019 and the 2020 Olympic Games.
BBC deputy political editor John Pienaar, who is in Hamburg, said: “The prime minister’s senior staff have made clear she means to promote the prospect of a new trading relationship with the US, picking up on her Trade Secretary Liam Fox’s talk of preliminary talks ahead of formal negotiations when the UK leaves the EU.
“That deal’s important, symbolically, and in terms of hard cash for Britain’s post-Brexit future – and ministers are keen to hold the US to past suggestions that Washington sees a trade deal as a priority.”
As she attends her first gathering of world leaders since the general election, Mrs May has dismissed suggestions that political and economic uncertainty from the UK’s decision to leave the EU and speculation about her own future is hampering the UK’s effort to lead on the world stage.
She rejected claims by former Foreign Secretary William Hague that the UK would lose influence on the world stage after Brexit.