Theresa May has insisted her Government is "batting for Britain" after the Brexit vote.
The Prime Minister, who is using a visit to New York to host a meeting of major US investors in an attempt to allay their fears about the UK leaving the European Union, acknowledged the process of breaking from Brussels would take some time.
But she said the UK could take advantage of the opportunities around the world that would come from Brexit.
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She was in New York for the United Nations General Assembly and a special summit on the migration crisis.
Mrs May said "uncontrolled migration" had to be tackled and warned that people travelling for economic reasons could undermine support for genuine refugees.
The Prime Minister's meeting with business leaders in the US comes amid concerns that overseas firms could move their European headquarters away from the UK after Brexit.
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Mrs May told broadcasters: "We have negotiations to go through for the UK leaving the EU. I am going to be ambitious in those negotiations. We want the right deal for the UK in terms of trade in goods and services and it will be a while before we come to an agreement on that deal.
"But what I think is absolutely crucial is that we recognise that coming out of the European Union gives us opportunities - opportunities to go out there around the world, be ambitious for the trade deals we want to do.
"I want the UK to be a global leader in free trade."
Mrs May, a cricket fan, added: "That's what this Government is doing, going out there around the world batting for Britain."
While in New York, Mrs May was hosting a round-table event for major US investors from industries ranging from banking to entertainment.
Firms represented at the event include Goldman Sachs, Morgan Stanley and Amazon.
She was also attending a reception for firms from the UK and US that are engaged in transatlantic trade.
"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 that will pertain once we have left the EU, we will be aiming to get the right deal for the UK."
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Mrs May used her first appearance at the UN to argue for a new approach to the migrant crisis, stressing that refugees should claim asylum in the first safe nation they reach and defending the right of countries to protect their borders.
She said: "I think that uncontrolled migration is not in the interests of the migrants themselves, it's not in the interests of refugees - who may find that they see less support as a result - it's not in the interests of the countries that people are coming from, travelling through or trying to get to.
"This is one of the great global challenges that we face and it is right that we deal with it as an international community and the UK will continue to show global leadership on this issue."
Her stance was criticised by the charity War Child, which works with youngsters in conflict zones.
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War Child head Rob Williams said: "Rather than getting too distracted by complex definitions of refugees and migrants and focusing on who to exclude, the Prime Minister could make a real difference by spearheading a global action plan for children forced to flee.
"This has to include the UK resettling a fair share of child refugees - especially unaccompanied minors - rather than suggesting that asylum should be granted only in the 'first safe country', which would shift virtually all responsibility to countries in the region.
"The UK can start by playing a much more active role in sorting out the desperate situation in the Calais camp and making sure the 600 unaccompanied children there are offered safety and support."
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