"In the light of the consultations I have conducted over the past days, I believe a short extension will be possible but it will be conditional on a positive vote on the withdrawal agreement in the House of Commons," Tusk told reporters.
Prime Minister Theresa May had asked the EU on Wednesday to delay Brexit until June 30 as she scrambled to contain a deepening political crisis, but faced warnings that Britain could still crash out of the bloc in nine days.
The pound plunged on currency markets as European Union leaders and British parliamentarians responded with scepticism to her request, made ahead of a Brussels leaders' summit on Thursday.
Exactly 1,000 days on from Britain's seismic 2016 referendum vote to leave the EU, a divorce deal negotiated by May is blocked in parliament and uncertainty grips the country.
She is seeking to put back the March 29 exit date to try one more time to get her agreement passed, but said any further postponement would undermine voters' trust.
In Paris, French Foreign Minister Jean-Yves Le Drian also had a tough message.
"A situation in which Mrs May is unable to deliver sufficient guarantees on the credibility of her strategy at the European Council meeting would lead to the request being refused and a preference for a no deal," he told parliament.
In her letter to Tusk -- addressed as "Dear Donald" -- May said she intended to bring her deal back to the Commons "as soon as possible", arguing that if it passed, she would need the delay until June 30 to implement the treaty.
If the text is rejected a third time, May said MPs would have to decide what happened next.
"As prime minister, I am not prepared to delay Brexit any further than June 30," she said, in comments interpreted as a hint about her own future.
She said delaying any longer would require Britain to hold elections for the European Parliament, which would be "unacceptable".
However, the European Commission, the EU's executive arm, said the June 30 date carried "serious legal and political risks".
In a phone call with May on Wednesday, Juncker urged her not to set a date that was beyond the European Parliament elections, due to be held between May 23rd and May 26th.