But a spokeswoman said May felt little pressure, having won the agreement of EU officials to take at least until the end of this year to come up with a negotiating stance for the talks that will shape Britain`s relationship with Europe and its future standing in the world.
"The main points that the prime minister made were about working together so that there was a smooth process for the UK leaving the European Union, that is why we are taking time to prepare for the negotiations," the spokeswoman told reporters.
"We want to see a strong European Union that we can have a strong relationship with once we have left."
Over breakfast, the two leaders agreed that Britain would have "a strong voice" in the EU while it was still a member and that it would stand firm on sanctions against Russia over its actions in Ukraine.
May has given little away on what she wants when Britain leaves the EU, saying she will not show her hand before Britain triggers Article 50 of the EU`s Lisbon Treaty to start the exit procedure. That will not happen this year, she says.
But while understanding the need for her new government to take time to get to grips with the complicated negotiations, some EU officials are keen to move quickly, fearing uncertainty over future relations is hurting investment.
Tusk who, as head of the European Council, leads the body that defines the bloc`s political direction and priorities, said on Twitter that it was "in everybody`s best interest to start ASAP (as soon as possible)."
UNFAZED
Britain`s economy, while slowing sharply, has recovered from the initial impact of the vote. Reports published on Thursday showed firms increasing the number of permanent staff and house prices rising.
Britain`s biggest consumer electricals and mobile phone retailer, Dixons Carphone (DC.L) was the latest company to say that its consumers seem unfazed by the Brexit vote.
Politicians who campaigned for Britain to leave the EU have taken the economic data as proof that the "remain" campaign had tried to frighten voters into staying by forecasting economic difficulties.
One, Liam Fox, who is now trade minister, said Britain was pressing on with plans to reach agreements with some of the world`s largest and fastest-growing economies. He told parliament the government had set up a working group with India to prepare for a post-Brexit trade deal.
May says reducing immigration into Britain is crucial after millions of Britons expressed their frustration in the vote over what they say is the stress on schools, hospitals and housing from high numbers of people settling in the country.
But the former interior minister, who was in charge of the ruling Conservative Party`s immigration policy, also says she wants the best trade deal for Britain, refusing to say whether the country will remain in the EU`s lucrative single market.
"It is in all our interests that there is a smooth departure, that we continue to work together, albeit with the UK on the outside, about how we can deliver economic growth, make sure that economic benefits are being spread around the country," her spokeswoman said.
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