Theresa May and her Australian counterpart Malcolm Turnbull have compared notes on their contacts with US President Donald Trump since his inauguration last month.
The two prime ministers spoke by phone on Thursday morning in a "substantial" conversation which also covered their hopes for a trade deal following Brexit, co-operation in the fight against Islamic State (IS) and relations with Iran, said Downing Street.
Reports earlier this month suggested that Mr Turnbull's first phone call with the US president was a stormy affair, with Mr Trump supposedly criticising a deal to take migrants from Australia as "the worst ever" and ending the conversation abruptly.
But Downing Street said the Australian PM was "very positive" about his contact with Mr Trump in his conversation with Mrs May, while both agreed that her trip to Washington as the first foreign leader to visit the new president in January had been "positive".
On Brexit, Mr Turnbull "reiterated Australia's commitment to maintaining a close partnership with the UK as we leave the EU", said the Number 10 spokesman.
"Both prime ministers said they looked forward to holding preliminary conversations on a comprehensive bilateral free trade agreement in due course."
Mrs May and Mr Turnbull, who were at Oxford University together, also discussed the campaign to defeat IS in Iraq and Syria and agreed on the importance of creating conditions to bring about long-term stability in Iraq.
Mrs May stressed the need for a political resolution in Syria excluding president Bashar Assad.
They discussed "the need to tackle Iran's destabilising influence in the region" and the importance of rigorous monitoring of the international deal on its nuclear programme.