LONDON, Oct. 8 -- British Prime Minister Boris Johnson will hold talks with his Irish counterpart Leo Varadkar later this week in a last ditch attempt to avoid a no-deal Brexit, a Downing Street spokesman said here Tuesday.

Johnson and the Irish prime minister spoke by telephone for about 40 minutes.

"Both sides strongly reiterated their desire to reach a Brexit deal," the spokesman said. "They hope to meet in person later this week."

The spokesman made the remarks as President of the European Parliament, David Sassoli, said there has been "no progress" following a meeting with the prime minister on Tuesday.

"I came here in the confident hope of hearing proposals which could take negotiations forward," he said. "However, I must note that there has been no progress" toward agreeing a new deal between Britain and the European Union ahead of the Oct. 31 deadline.

Sassoli told Sky News that Johnson said to him that he "will not ask for an extension."

Johnson vowed to take his country out of the European Union on Oct. 31, with or without a deal.