The European Council president travelled to London to meet Theresa May this afternoon.
The summit marks the Prime Minister's first face-to-face meeting with Mr Tusk after she formally triggered two years of withdrawal talks when she invoked Article 50 of the Lisbon Treaty last week.
Speaking this morning in Nottingham, Mrs May said: "I'm going back to London to meet President Donald Tusk and we will be talking about the start of negotiations, how we're going to take these negotiations forward.
"I've obviously sent the letter to invoke Article 50. We've said very clearly we want to maintain a deep and special partnership with the EU and I think that has been reciprocated.
"I'll be talking with President Tusk about how we can ensure within the timescale that we've got that we can deliver a deal that is going to work for the people of the UK but I also believe that will be a deal that will work for the EU as well."
Mr Tusk has made it clear he is seeking a fair settlement, but warned the Brexit negotiations could become confrontational at times.
In pictures: Theresa May meets with EU's Tusk Thu, April 6, 2017
The two leaders held talks on Brexit negotiations
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British Prime Minister, Theresa May and The Chairman of the European Union, Donald Tusk, meet inside 10 Downing Stree
Donald Tusk is meeting Prime Minister Theresa May at Number 10 today in London to discuss way ahead on Brexit
Donald Tusk spokesman
Mr Tusk’s spokesman Preben Aamann confirmed the meeting.
He said Mr Tusk will meet the Prime Minister at Number 10 today “to discuss way ahead on Brexit”.
The European Council president insists Brussels will take a “constructive” approach to negotiations and says the EU wants to keep the UK as a "close partner" on trade and security in the future.
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Theresa May will meet Donald Tusk today hours after arriving back from her Middle Eastern tour
He dealt a blow to the Prime Minister earlier this week by blocking attempts to hold parallel divorce and trade talks.
Mr Tusk said: “Once, and only once we have achieved sufficient progress on the withdrawal, can we discuss the framework for our future relationship."
High on the agenda is expected to be securing the rights of EU citizens on both sides of the new UK-EU frontier as well as the controversial divorce bill.
Theresa May and Donald Tusk have met in Downing Street
Mr Tusk said: "We will need to make sure that the UK honours all financial commitments and liabilities it has taken as a member state.
"It is only fair towards all of those people – communities, scientists, farmers and so on – to whom we, all the 28, promised and owed this money.
"I can guarantee that the EU, on our part, will honour all our commitments."
The meeting comes as Theresa May arrives back from the Middle East
Donald Tusk accepted the Article 50 letter last week
The European Parliament insisted Britain must meet all its financial obligations and rejected any "cherry-picking" of privileged access to the single market for sectors of the UK economy such as financial services.
The draft resolution insists Britain must meet all its financial obligations to the bloc, which some estimates have put as high as £56 billion.
Mr Tusk's meeting comes just hours after Mrs May arrived back in Britain following a three-day trade trip to the Middle East.
Brexit day: images from around the country as Britain invokes Article 50 Mon, April 3, 2017
The country reacts as Theresa May officially invokes Article 50, and begins the process of Britain leaving the European Union
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Pro-EU demonstrators protest outside Parliament
The busy Prime Minister arrived back last night and is due to give a speech in Nottinghamshire this morning.
She will then travel back to Downing Street to meet with Mr Tusk for the first time in person since triggering Article 50.
Mrs May spent three days visiting Jordan and Saudi Arabia to discuss trade and security issues.