Despite continuous efforts and growing common grounds of Britain and the European Union (EU), it was not possible to reach a complete agreement Monday, said EU Commission President Jean-Claude Juncker in a hastily arranged press conference with visiting British Prime Minister Theresa May.

"This is not a failure. This is the start of the very last," he added, extending EU's deadline by pledging to resume their talks later this week.

Calling May as a tough negotiator in his 2-minute briefing, Juncker said he is confident that sufficient progress could be reached before the EU summit slated for Dec. 15.

Echoing Juncker's optimism, May told reporters in her one-minute speech that "we will conclude this positively."

"Crucially it is clear that we want to move forward together, but on a couple of issues, differences do remain, which require further negotiation and consultation," said May before heading to meet President of the European Council Donald Tusk almost one-hour late than scheduled.

Prior to May's Brussels trip, expectations were high for breakthroughs on three major Brexit issues, namely the divorce bill, Irish border and citizen's rights.

Some British media even reported that British government is said to have agreed there will be continued "regulatory alignment" between the Irish Republic and the Northern Ireland.

This would mean, in effect, that Northern Ireland would continue to abide by all EU rules on trade and customs, said the reports.