With the deadline for the UK's departure from the European Union looming and no deal yet agreed, the European Council President gave an indication of how strained things are behind the scenes by publicly accusing UK Prime Minister Boris Johnson of playing games.

In an exasperated tweet posted on Tuesday, Donald Tusk said Johnson did not want a deal, was not acting in the best interests of the British people, and was putting the security of the public at risk.

He tweeted: “.@borisJohnson, what's at stake is not winning some stupid blame game. At stake is the future of Europe and the UK as well as the security and interests of our people. You don't want a deal, you don't want an extension, you don't want to revoke, quo vadis [where are you going]?”

.@BorisJohnson, what’s at stake is not winning some stupid blame game. At stake is the future of Europe and the UK as well as the security and interests of our people. You don’t want a deal, you don’t want an extension, you don’t want to revoke, quo vadis?

— Charles Michel (@eucopresident) October 8, 2019

Tusk's tweet comes after Downing Street appears to have given a series of briefings to journalists implying that a deal will not be reached.

A number of UK-based media outlets have reported No. 10 sources as saying a Brexit deal is “essentially impossible” following a phone call between Johnson and German chancellor Angela Merkel on Tuesday morning. CNN has asked Downing Street for comment.

A German government spokesman told CNN that details of the conversation would not be made public.

“As is customary, we don't report from such confidential conversations,” the spokesman said.

Johnson unveiled his Brexit blueprint on October 2, which was greeted with cautious optimism from hardliners within his own Conservative party but dismissed by many European officials as a non-starter.

The next summit of EU leaders is on October 17 and 18 and time is running out for both parties to negotiate a new deal by the latest Brexit deadline of October 31.

If the PM doesn't get a deal by October 19, he is obliged by law to seek a new extension to the Brexit process. But Johnson has long maintained that he would take the UK out of the European Union on October 31 “do or die.”

Eliza Mackintosh contributed to this report.