In her first foreign trip as prime minister, Ms Truss will meet the two against the backdrop of Brexit tension and questions over whether she regards the French leader as a “friend or foe”.
Ms Truss hopes the focus will be largely on energy security and helping Ukraine in its war against Russia, but clashes over the Northern Ireland Protocol are bound to feature.
Mr Biden, who has proud Irish heritage, has raised concerns about Brexit’s threat to the peace process and played down the chances of a free-trade deal with the UK.
Mr Macron has long been a critic of Brexit and has been firm in pressing the UK to keep to commitments on Northern Ireland and fishing rights.
Ms Truss sparked a diplomatic row during the Tory leadership contest when she declined to give a clear answer as to whether Mr Macron was a “friend or foe”.
Instead, the then-foreign secretary said last month that the “jury’s out”.
Asked if the meeting with Mr Macron would be uncomfortable, the spokesman said: “No, the prime minister wants to build a constructive relationship with President Macron.”
But he maintained the position on the Northern Ireland Protocol Bill, which the EU and others say will break international law.
Ms Truss will meet Mr Macron and Ms von der Leyen on Tuesday, before seeing Mr Biden on Wednesday.
She had been set to talk to Mr Biden in Britain at the weekend as he visited for the queen’s funeral, but the meeting was postponed.
Ms Truss is not scheduled to receive the White House invitation Boris Johnson was given during his visit to UNGA last year.
Ms Truss will warn that now is not the time to “take our foot off the gas” in opposing Vladimir Putin’s invasion of Ukraine.
“We will continue to act to restore sovereignty and self-determination to Ukraine because this isn’t just Ukraine’s fight," her spokesman said.
"The whole world suffers when a regime like Putin’s is allowed to bully and blackmail its neighbours."
Ms Truss will try to use the visit to “spur further international action to end energy dependence on Russia, making sure the world is never in this position again”.
“In the short term, that means increasing the supply of gas and other sources of energy, and in the long term, it means democracies tapping into our shared resources, natural, technological and entrepreneurial to develop alternative sources of energy.”
Before leaving the US on Wednesday evening, Ms Truss will use her summit speech to say the UK under her leadership will be “an active defender of our democratic values”, and will work to counter authoritarianism with allies.
The trip begins a frantic few days of political action in Ms Truss’s fledgling premiership, with details on how businesses will be helped through the energy crisis and a major announcement on the National Health Service.
Ms Truss, who was being joined by Foreign Secretary James Cleverly in the US, will then return before Chancellor Kwasi Kwarteng’s mini-budget on Friday.
Labour urged her to use the trip to start “rebuilding our country’s diplomatic influence”.
“Twelve years of Conservative governments making diplomatic gaffes, announcing plans to break international law, failing to live up to promises on climate action and cutting international aid have damaged relations with the US and left Britain isolated on the global stage," said shadow foreign secretary David Lammy, who was also attending UNGA.
“After being snubbed by the Biden administration within her first weeks in office, Liz Truss urgently needs to wake up to the damage her reckless approach to foreign policy is doing to the UK’s national interest.
“The prime minister must use the UN General Assembly to bring the UK back in from the cold and begin rebuilding our country’s diplomatic influence.”
Mr Cleverly will call for action on Russian behaviour in Ukraine in meetings with other foreign ministers, including US Secretary of State Antony Blinken and Ukraine's Dmytro Kuleba.
On Thursday, he will take part in a foreign minister-level UN Security Council meeting focused on the Russian invasion.