The European Council president said reciprocal guarantees, which would also provide security for Brits living in Europe, were key issues to be addressed before talks turn to trade deals.
Mr Tusk and European Commission president Jean Claude Juncker both highlighted the importance of the matter as leaders of EU member states agreed on their joint negotiating strategy for talks set to commence after the 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 took just a matter of minutes to decide on their joint approach.
President Tusk tweeted the outcome of their discussions, saying: "Guidelines adopted unanimously. EU 27 firm and fair political mandate for the Brexit talks is ready."
A key element is the "phased" approach – with leaders insisting a future trade deal will only be considered later on in Brexit negotiations.
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.
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."
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 we have already prepared a text which could be adopted immediately if our British friends would be ready to sign it," he said.
"That will probably not happen."
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, saying: "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."