David Cameron arrives at the United Nations on Sunday hoping to work with other countries on a deal to end Syria’s bitter civil war, a deal that could allow its president, Bashar al-Assad, to stay in power for an interim period.

The prime minister, who arrives in New York for a UN summit aimed at curbing global poverty, backs the view of his foreign secretary, Philip Hammond, that Assad must ultimately step down but could remain for a while as part of a transitional government.

Hammond told the Commons foreign affairs committee several weeks ago that Assad could be allowed to stay for up to six months, but a government source said Downing Street does not have a specific timeframe in mind, raising the possibility it could be longer.

A British government source said: “The prime minister’s view is that there is not a long-term, stable, peaceful future for Syria where Syrian people can return home with President Assad as its leader, and that’s what we’ve got to work towards … We would be open to working with other countries on a solution whereby there is a transition. We haven’t got a specific timeframe for when we think Assad should go. We’ve always been clear that there would need to be some sort of transition.”

Russia’s continued backing for Assad, including the dispatch of troops and aircraft to Syria last week, appears to be forcing the west to reconsider its position on the four-year civil war, in which the dictator is battling Islamic State and a wide variety of other insurgent groups. The UN general assembly in New York offers an opportunity for world leaders to inject new momentum into international talks on Syria, especially as attendees include US president Barack Obama and Russian president Vladimir Putin.

The prime minister has issued a robust defence of his approach to the Syrian refugee crisis and other humanitarian challenges across the world ahead of the summit. In an exclusive article for the Observer, he argues that the UK’s multibillion-pound overseas aid programme has provided “life-saving support” to millions of people displaced by the conflict in Syria.

Cameron says the UK aid payments, now totalling around £12bn a year, allow this country to meet its moral obligations and respond fast to global challenges as they arise.

Writing on the eve of the Labour party conference, where he will face criticism for reacting too slowly to the refugee crisis, Cameron insists his commitment to spending 0.7% of GDP every year on overseas aid puts the UK on the high ground and allows it to take the lead in humanitarian responses.

Throughout Cameron’s premiership his commitment to the 0.7% policy – which was finally enshrined in law in March this year – has attracted strong criticism from rightwing Tory MPs, who have argued that much of the money is wasted and would be better spent in the UK at a time of austerity. Cameron has also been attacked recently from the left – and by church leaders – for a slow and insensitive initial response to the refugee crisis.

Taking on his critics from both sides, the prime minister argues that the huge sums committed to aid allow the UK to respond flexibly and speedily to crises, while also directing money to economic development andthe spread of democracy.

“We have helped to set the agenda,” Cameron writes. “We fought hard to keep tackling extreme poverty as the clarion call for the world. We were determined that issues like gender equality and tackling climate change would be an integral part of the goals.

“And we made sure there was a proper focus on the causes of poverty – like corruption – as well as its symptoms. For the first time ever, we have got proper references to good government, the rule of law and access to justice. Above all, because we kept our promises on aid spending, others listen to us.

“We need aid to provide life-saving support for refugees in Syria and neighbouring countries so they don’t embark on perilous journeys to Europe. We need aid to tackle epidemics like Ebola in west Africa, saving hundreds of thousands of lives and preventing it spreading around the world. We need aid to shore up stability in countries like Somalia, helping to protect the people there and preventing these places becoming safe havens for terrorists.”

Between 2010, Cameron’s first year as prime minister, and 2013, overseas aid rose by £3.01bn to £11.46bn. In April last year, the UK reached its goal of spending of 0.7% of GDP on aid, becoming the first G8 country to do so.

His comments in the Observer will be seen as an attempt to reach out to centre-ground voters with a message about compassionate Conservatism.

In his first speech as Liberal Democrat leader,Tim Farron tore into Cameron last week for his response to the refugee crisis, saying he had put in the “minimum effort for the maximum headlines”. Farron said Cameron’s plans to take in 20,000 people fleeing the Syrian civil war by 2020 would not help a single refugee already in Europe and criticised him for not taking part in the EU quota system.