The European Council president said reciprocal guarantees, which also provided certainty for British ex-pats living on the continent, were foremost among issues to be addressed before talks turned to future trading terms.
Mr Tusk and European Commission president Jean Claude Juncker both flagged the importance of the matter as leaders of the EU 27 formally endorsed the bloc’s negotiating strategy for talks set to commence after next month’s UK General Election.
“This must be the number one priority for the EU and the UK,” said Mr Tusk.
Apart from a few small amendments, the final negotiating framework mirrored the proposals outlined in draft form by Mr Tusk last month.
The leaders of the member states remaining in the EU took only minutes to approve the joint strategy at a special summit meeting in Brussels on Saturday.
Central to it is the “phased” approach, with EU leaders insisting the shape of a future trading relationship can only be considered when progress is made on the terms of the UK’s departure.
Along with citizens’ rights, the disputed “divorce bill” the UK will have to pay on exit - estimated at a potential £50 billion - and the thorny question of how to maintain a free-flowing Irish border are also key “phase one” issues for the EU.
Mr Tusk said “sufficient progress” on all of those were needed before the EU’s future relationship with Europe could be addressed.
Reacting to the summit outcome while on an election campaign visit to Scotland, Prime Minister Theresa May said both sides of the process now had their negotiating guidelines mapped out, with the UK’s position having been made clear in her letter triggering Article 50.
In a pitch for votes, Mrs May said what mattered was the need for a strong prime minister with a strong mandate sitting at the Brexit negotiating table.
“It’s a very simple choice, strong and stable leadership under me and my team or a coalition of chaos under (Labour leader) Jeremy Corbyn and I know which one is going to get the best deal from Brexit and the European Union,” she said.
Mr Tusk said EU officials had compiled a “precise and detailed” list of the citizens’ rights the union wanted protected. The council president urged Theresa May to sign off on the proposals.
“In order to achieve sufficient progress we need a serious British response,” he said.
“I want to assure you that as soon as the UK offers real guarantees for our citizens we will find a solution rapidly.”
Mr Juncker and the EU’s chief negotiator Michel Barnier met the Prime Minister in Downing Street earlier this week.
After Saturday’s summit, the commission president said the UK was underestimating the technical difficulties of Brexit and warned it would take a huge amount of time to reach agreement on apparently single issues.
In regard to EU nationals living in the UK, he challenged Mrs May to sign up to the commission document on its desired guarantees, but admitted he did not think she would.
“So this will take time and if we want to be precise and to deliver guarantees to citizens, this will take a huge amount of time, although as a Commission and as Michel Barnier (the EU’s chief Brexit negotiator), we have already prepared a text which could be adopted immediately if our British friends would be ready to sign it like that. That will probably not happen,” he said.
The Irish element of the Brexit process is set to assume major significance when negotiations start - with the border identified among the trio of crucial initial sticking blocks that need to be navigated.
Irish premier Enda Kenny said it was a huge endorsement of his government’s lobbying efforts that resolution of the issue had been placed at the top of the EU wish list.
The taoiseach said a solution would require ingenuity and imagination.
“That’s what minds will be applied to now over the next number of months,” he said.
Aside from dealing with the current Irish border, the European Council also provisionally agreed its approach if the day came when the people of Northern Ireland voted to end partition and join a united Ireland.
While not part of the Brexit negotiating guidelines, EU leaders accepted a statement proposed by Mr Kenny that, in the event of unification, Northern Ireland would automatically assume the EU membership already held by the Republic of Ireland, rather than having to reapply.
That position will be formally adopted at the next EU council meeting next month.
During his post-summit comments, Mr Juncker also brushed off suggestions that his working dinner with Mrs May at Number 10 had gone badly.
But he appeared to criticise the food on offer as he reiterated his point that Brexit cannot happen “just like that”.
“It will take time and we have to discuss a certain number of the elements we will have to address in the next coming months,” he said.
“But it was excellent (the dinner) - I’m not talking about the food.”
Mr Tusk and Mr Juncker both stressed the unity of the EU 27, with the commission president revealing that leaders took just four minutes to sign up to the negotiating guidelines.
Mr Juncker added: “It was surprising given the past experiences, that we could get an agreement this swiftly, and such a solid agreement among the 27 that fast.”
Mr Tusk said it was vital for the 27 to continue to speak with one voice.
“It is only then that we will be able to conclude the negotiations which means that our unity is also in the UK’s interest,” he said.
“As for now, I feel strong support from all the EU institutions, including the European Parliament, as well as all the 27 members states.
“I know this is something unique, but I am confident that it will not change.”