Mr Tusk told reporters that all EU 27 members agreed unanimously that "the withdrawal agreement is not open for renegotiation".
He joked that the next round of Brexit might be “more exciting” due to personal feelings in London, a reference to the inevitability of a ‘hard-Brexit’ candidate in 10 Downing Street.
He also said that the EU wants an “orderly Brexit”.
However, he explained that future UK-EU relations could be discussed if the UK government's position were to “evolve”.
Other top EU officials echoed Mr Tusk's caution on Friday claiming that the withdrawal agreement would not be subject to any adjustments.
An EU official said: "It is the best possible deal. We will not start to renegotiate again without having a reason to delay."
Prime Minister Xavier Bettel of Luxembourg echoed the statement from Brussels, saying that the EU would not be willing to offer a new Brexit deal even after a new UK prime minister is picked.
These statements follow a deadlock between EU politicians, who were unsuccessful in attempts to declare candidates for leading EU positions, including the successor to Jean-Claude Juncker as president of the European Commission.
In a parallel to the UK’s own domestic politics, Mr Bettel said that there is “no majority in the European Parliament”.
The EU body will reassemble on 30 June with the hope of deciding nominations for the new president.
Having passed through rounds of MP-exclusive votes, one of the two remaining candidates for Tory leader will now face a ballot for the Conservative Party membership of 120,000 before one succeeds caretaker Prime Minister Theresa May on 22 July. After five votes, Conservative lawmakers have narrowed down the choice to two candidates, Boris Johnson and Jeremy Hunt. At the next round, all members of the party rather than just those with seats in the parliament, will vote.