European Council President Donald Tusk arrives at EU headquarters prior to an EU Summit in Brussels, Belgium, Dec. 14, 2017. (Xinhua/Ye Pingfan)

STRASBOURG, France, Jan. 16 (Xinhua) -- Despite "sufficient progress", European Council President Donald Tusk told European lawmakers in Strasbourg on Tuesday that the most difficult part of the process was still to come.

"The hardest work is still ahead of us, and time is limited," Tusk said in his report to members of European Parliament (MEPs) on the outcomes of the December 2017 European Summit.

"We must maintain the unity of the EU27 in every scenario, and personally I have no doubt that we will," he said.

"If the UK government sticks to its decision to leave, Brexit will become a reality -- with all its negative consequences -- in March next year. Unless there is a change of heart among our British friends," Tusk told lawmakers.

"What we need today is more clarity on the UK's vision," the European Council President said. "Once we have that, the leaders will meet and decide on the way the EU sees its future relationship with the UK as a third country."

Tusk appeared to offer hope to anti-Brexit campaigners, concluding his remarks by referencing the ability for a democracy to change its mind. "We, here on the continent, haven't had a change of heart. Our hearts are still open to you," he said.

Tusk repeated his stance later with a tweet.

Also addressing MEPs in the same debate, European Commission President Jean-Claude Juncker echoed his European Council colleague, saying "Mr. Tusk said our door remains open, and I hope that will be heard clearly in London."

The discussion in Strasbourg, part of the European Parliament's January 2018 plenary session, came on the heels of a new round of Brexit negotiations launching on Monday evening.

European media have reported that leaked draft guidelines given to the EU's chief negotiator, Michel Barnier, include tough new stances on European citizens' rights, and continued EU regulations during the called-for transition period after March 2019, when Britain would become a third country.

Guy Verhofstadt, the European Parliament's representative on Brexit issues, told MEPs on Tuesday morning that "We are coming to the most difficult part of this negotiation".

"We need rock solid guarantees" on citizens' rights, he said and later tweeted.

Verhofstadt also insisted that throughout the duration of the transition period, Britain would be required to observe EU law entirely, and that any procedure for the residency of European citizens could only begin at the conclusion of the transition period.

This appears to support leaks that the EU is demanding that any European citizen who moves to Britain before 2020 be given permanent residency rights.

"The European Parliament won't allow cherry-picking in the Brexit transition. All EU legislation, all EU policies will continue to apply. The only exception is that Britain will no longer be represented in the institutions that decide on legislation and policies," Verhofstadt said.

One of the most difficult issues embedded in the transition period relates to migration, with the EU reportedly demanding that its "freedom of movement" principle continue to apply during the transition period, which would block Britain from immediately introducing strict new controls on new arrivals to Britain.

Manfred Weber, leader of the European People's Party group, warned that his political family would not support a final Brexit deal if the conditions were not good enough, indicating that his party also felt that difficult work remained in the negotiations.

"My message to London is please stop complaining, please deliver," Weber said.

Britain evoked Article 50 of the Treaty on European Union in March of 2017, triggering a two-year negotiation period for a divorce from the bloc. Talks are limited by law to two years, with Britain scheduled to become a third country on March 29 of 2019.