The PM will also say refugees should claim asylum in the first safe country they reach and stress that nations have a right to control their borders.
The UN says a record number of people have been displaced by conflict.
It estimates that 65.3m people were either refugees, asylum seekers or internally displaced at the end of 2015, an increase of 5m in a year.
The UN summit for refugees and migrants is aiming to agree a “more humane and coordinated approach”.
Mrs May will warn “unprecedented levels of population movement” risks undermining public confidence in the economic case for legal migration.
She will argue that refugees should seek asylum in the first safe country they arrive in because the current trend of onward movement exposes them to increased danger and benefits criminal gangs.
Such an approach would bar EU countries from allowing migrants to travel onwards from countries like Greece, Italy and France through Europe to Britain.
Speaking ahead of the summit, Mrs May said resources should be focused on “refugees in desperate need of protection”.
She said the UK was “already playing its part” but promised to “step up our efforts” with more financial assistance.
“But we cannot simply focus on treating the symptoms of this crisis, we need to address its root causes too.
“While we must continue our efforts to end conflict, stop persecution and the abuse of human rights, I believe we also need a new, more effective global approach to manage migration.”
Defending the UK’s approach, the Home Office said the government had pledged £2.3bn in humanitarian aid to Syria and neighbouring countries and are providing nearly £70m in response to the Mediterranean migration crisis.
“This government has been at the forefront of the international response to the humanitarian crisis in Syria,” it said.
“We have committed to resettling 20,000 Syrian refugees through our Vulnerable Persons Resettlement scheme over the course of this parliament – we are on track to achieve that and have already provided refuge to more than 2,800 under this route.
“Under the new Vulnerable Children’s Resettlement Scheme we will also bring 3,000 individuals to the UK over the same period.”
As well as speaking at the UN event, chaired by secretary-general Ban Ki-moon, Mrs May will also take part in a summit on refugees hosted by US president Barack Obama on Tuesday.
In London’s Parliament Square, campaigners have created a display using lifejackets worn by refugees crossing the sea into Europe.
Charities behind the temporary installation said it would “remind leaders of the risks families have taken to reach safety, the need for solidarity with refugees, respect of their rights and more international responsibility sharing”.
They said the summit was a “historic opportunity to garner the political will of world leaders to save lives, protect rights and share responsibility on a global scale”.