"I don't expect any kind of breakthrough tomorrow -- we have to work really hard in between October and December to finalize this so-called first phase and to start our negotiations on our future relations with the UK," Tusk said Wednesday.
"I am absolutely sure that it's still possible to achieve this final of first phase in December but for this we need more concrete proposals from the British side to be honest," Tusk added.
Leaders of the other 27 EU member states meeting in Brussels this week are set to postpone until December a decision on whether enough progress has been made in Brexit talks to move on to discussing a future relationship between the EU and UK.
Fears are growing that London may fail to strike a withdrawal agreement with Brussels before its formal departure on March 29, 2019.
The UK had hoped the summit -- where British Prime Minister Theresa May will plead her case at a working dinner -- might clear the stalemate.
EU leaders have voiced frustration over what seems to be London’s reluctance to cover the expenses for its exit from the bloc.
Underscoring the increasingly tense atmosphere around the talks, European Parliament president Antonio Tajani voiced his frustration on Tuesday, warning Britain that it must be more "realistic" on its offer of the financial settlement.
May has promised to maintain Britain's contributions to the EU for two years after Brexit in March 2019 to complete the current EU budget period, totaling around 20 billion euros ($24 billion).
"Twenty billion is peanuts. The problem is 50 or 60 (billion euros), this is the real situation," Tajani said during a BBC interview.
May accused of delaying contested Brexit bill
UK’s main opposition Labour Party has accused the government of delaying debate of the EU (Withdrawal) Bill, also known as the Brexit bill, which will end Britain's EU membership.
"This is further proof that the government's Brexit strategy is in paralysis," Labour's Brexit spokesman Keir Starmer said in a statement on Tuesday.
“The negotiations are in deadlock and now a crucial piece of legislation is facing further delay," he said, adding that this cast doubt on "whether the prime minister can deliver Brexit."
A Labour source told AFP that the withdrawal bill, which aims to provide legal certainty after Brexit, may not pass the House of Commons in Parliament until early 2018