At the UN General Assembly in New York, she insisted countries have a right to control their borders and said refugees should claim asylum in the first safe country they reach.
The Prime Minister warned that “unprecedented levels of population movement” could undermining confidence in rules governing legal migration and blur the distinction between refugees and migrants.
Allowing migrants arriving in the EU to move from countries like Greece and Italy onwards into the continent exposed them to greater danger from criminal gangs, Mrs May said.
She said resources should be focused on “refugees in desperate need of protection” and argued that the UK was “already playing its part”. She pledged to “step up our efforts” and spend more money supporting countries affected by mass migration.
“But we cannot simply focus on treating the symptoms of this crisis, we need to address its root causes too,” she said.
“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.”
The Prime Minister was among the world leaders who have arrived at the UN amid tight security following the bomb attack in Manhattan.
She will take part in another high-level summit on the migrant crisis hosted by US President Barack Obama today, and is also taking the opportunity to meet key US businesses with investments in the UK in an effort to allay their concerns about Brexit.
Ahead of the summit, she told reporters on the RAF Voyager taking her to New York: “We have always taken the view in relation to helping Syrian refugees that, actually, we can help all Syrian refugees by putting aid into the region. We are the second biggest humanitarian donor, we have a very proud record – there will be Syrian children being educated, people with medical supplies, with water, with food, as a result of the efforts that the UK taxpayer has put in through our donations.
“We are taking the 20,000 from the Syrian vulnerable persons relocation scheme but we also are taking Syrians in through other routes as well – through the normal asylum seeking route, [and] 3,000 vulnerable children from the region, some of whom will be Syrian, some will not be.”
Jordan’s foreign minister Nasser Judeh lashed out at wealthy countries that have not taken in even a handful of refugees.
Speaking at the summit, Mr Judeh said that his country was hosting 1.3 million refugees from the Syrian conflict – equivalent to 20 per cent of Jordan’s population – while larger and wealthier countries had not even received “a handful”.
He said the plight of migrants from the seven-year Syrian conflict brought “shame” on the international community. Mr Judeh called for more funding to help Jordan bear the cost of hosting refugees, expedited resettlement of refugees in third countries and a political settlement to the Syrian conflict.
The Home Office defended the government’s record on migration, saying it had pledged £2.3 billion in aid to Syria and was providing £70 million to tackle the migration crisis in the Mediterranean.
“This government has been at the forefront of the international response to the humanitarian crisis in Syria,” the Home Office 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.”
Mrs May will meet Japanese prime minister Shinzo Abe for talks today, just weeks after his government produced a 15-page dossier listing his country’s firms’ concerns over Brexit.
The Prime Minister will host a round-table event for major US investors from industries ranging from banking to entertainment.
Firms represented at the event will include Goldman Sachs, Morgan Stanley and Amazon.
She will also attend a reception for firms from both the UK and US that are engaged in transatlantic trade.
“What I will be talking about with both American and British business leaders is about how we can encourage that trade and investment between the two countries,” Mrs May said.
“Something like a million people in the UK wake up each morning and go to work for an American company in the UK.
“I will be talking to them and hearing from them what their emphasis is in terms of the issues that they want us to address, but when we go into the negotiations for the trading deal with the European Union, we will be aiming to get the right deal for the UK.”