PM hails 'very positive' Brexit talks with Tusk

"There are still issues across the various matters that we're negotiating on to be resolved, but there's been a positive atmosphere in the talks and a genuine feeling we want to move forward together," May said after talks with Tusk on the margins of an EU summit in Brussels.

The British premier met Tusk, German Chancellor Angela Merkel and other leaders on the sidelines of the summit with ex-Soviet states as part of a bid to unlock negotiations on a future trade deal.

May said they were making progress on all of the major issues -- Britain's exit bill, the rights of EU nationals living in Britain and the Irish border, which has flared up as a major sticking point in recent weeks.

"In relation to the border between Northern Ireland and the Republic of Ireland, we and the Irish government continue to talk about the solutions for that," May said.

"We have the same desire. We want to ensure the movement of people and trade across that border can continue as now and we don't create any new barriers to trade or the movement of people across that border."

European Commission President Jean-Claude Juncker said he was more confident than before about a deal but added nothing would be decided before he had dinner with May on December 4.

Tusk said after the talks that a deal in December was possible, but still a "huge challenge".