Ahead of her first meeting with US President Joe Biden, Truss also conceded that a post-Brexit UK-US trade deal was unlikely for years.
“There aren’t currently any negotiations taking place with the US and I don’t have an expectation that those are going to start in the short to medium term,” she told reporters en route to New York.
At the UN, Truss is also due to meet EU commission chief Ursula von der Leyen, having met French President Emmanuel Macron.
Like Biden’s White House, they are unhappy with her hard line on Brexit and Northern Ireland.
During their meeting, Truss thanked Macron “for his kind words following the passing of Her Late Majesty The Queen,” according to a statement from her Downing Street office.
The pair agreed on the need to continue backing Ukraine and also to enhance UK-France cooperation on energy with a difficult winter looming.
Truss earlier vowed to rally Western support at the UN over Ukraine, saying her government would match or exceed the £2.3 billion (B96.5bn) it plans to extend this year.
“Ukraine’s victories in recent weeks have been inspirational,” she said in a statement, after Kyiv’s forces pushed the Russian invaders out of almost all of the Kharkiv region in a lightning counter-offensive.
“My message to the people of Ukraine is this: the UK will continue to be right behind you every step of the way. Your security is our security.”
Boris Johnson’s successor flew out of London hours after delivering a biblical reading at Monday’s funeral of Queen Elizabeth II, as government mourning ends and UK political life resumes in full speed.
The late monarch appointed Truss as her 15th prime minister on Sept 6, in one of her final ceremonial acts as head of state. She died two days later.
Truss said she was “hugely honoured” to be appointed, and praised the “huge outpouring of love and affection” shown towards the queen, as well as the “huge amount of warmth towards” her successor King Charles III.
But Charles’s new reign, and Truss’s administration, start under a darkening economic cloud due to a cost-of-living crisis brought on by Russia’s war in Ukraine that is hurting millions at home.
She is due back in London on tomorrow, a day before finance minister Kwasi Kwarteng delivers an emergency budget statement after the government vowed a costly scheme to cap rocketing energy bills.
Culture Secretary Michelle Donelan denied that the financial crisis could force a re-think of the UK’s aid to Ukraine.
“We are not re-evaluating our support in the Ukraine, we are doubling down on our support in the Ukraine,” she told Sky News.