With the two sides exchanging barbs about who is to blame about the sluggish pace of the negotiations, EU chief negotiator Michel Barnier separately reminded London that "Brexit is not a game".
Former Polish premier Tusk appeared to dash London's hopes that EU leaders will use a summit on October 19 to agree to move on from divorce talks to the next phase of negotiations, dealing with a future relationship.
He insisted that Brussels was still working towards a deal, despite British Prime Minister Theresa May saying her government is making preparations in case there is no accord when Britain leaves the EU in March 2019.
"We hear from London that the UK government is preparing for a 'no deal' scenario. I would like to say very clearly that the EU is not working on such a scenario," Tusk told the EU Committee of the Regions in Brussels.
"We are negotiating in good faith, and we still hope that the so-called 'sufficient progress' will be possible by December," he added.
"However, if it turns out that the talks continue at a slow pace, and that 'sufficient progress' hasn't been reached, then -- together with our UK friends -- we will have to think about where we are heading."
May told the EU on Monday that the "ball is in their court" after she unveiled a range of Brexit compromises in a speech in Florence in September, and called for a two-year transition period.
'Brexit is not a game'
Britain also on Monday outlined proposals for new laws to set tariffs and quotas including if Britain leaves the European Union with no agreement in place, as it prepares for a post-Brexit customs system.
Britain and the EU are this week holding a fifth round of Brexit divorce negotiations, the last before next week's EU summit to decide on whether there is "sufficient progress" in the talks.
The EU insists on progress on Britain's Brexit bill, the rights of three million EU citizens living in the UK, and the fate of the border in Northern Ireland, before talking trade as Britain wants.
But this week's four-day talks have got off to a slow start, with Barnier and his British counterpart David Davis meeting only on the second day of negotiations, where they would normally meet on the first.
After a lunch of sea bass, Scottish beef and English and French sparkling wine, Barnier Barnier told Britain's BBC and Sky News: "The lunch was good and we had constructive talks."
Asked if the ball was now in the EU's court, the Frenchman replied: "Brexit is not a game. Don't forget."
The two sides also sniped at each other over the fact that Wednesday's official talks schedule remains empty.
"Our teams are available 24/7 and the timing of talks depends on the availability of our UK partners," European Commission spokesman Margaritis Schinas said when asked why Wednesday's timetable was blank.
A British government spokesman hit back, saying both sides had kept Wednesday free "from the outset" to give flexibility to have technical talks.
"The UK has always been available for that and it simply incorrect to suggest otherwise," the spokesman said.
Officials later said some British and EU negotiators would in fact be sitting down to technical talks on Wednesday, without giving further details.
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