In a letter to the other 27 European Union leaders ahead of a key summit on Saturday, Tusk said that "before discussing our future, we must first sort out our past".
The EU 27 are set to adopt guidelines for the negotiations on Brexit at the summit, following British Prime Minister Theresa May's formal triggering of the two-year divorce process last month.
Former Polish premier Tusk said the "only possible approach" was phased talks, in which Britain must make "sufficient progress" on the divorce issues before negotiations on future ties.
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"This is not only a matter of tactics, but - given the limited time frame we have to conclude the talks - it is the only possible approach," Tusk wrote to the leaders.
"I would like us to unite around this key principle during the upcoming summit, so that it is clear that progress on people, money and Ireland must come first," he wrote.
"And we have to be ready to defend this logic during the upcoming negotiations."
May wants to discuss the divorce settlement and a trade deal at the same time ahead of Britain's exit from the bloc in March 2019.
'Commitment to unity'
The EU says the key issues are the fate of three million EU citizens living in Britain and one million Britons resident in the EU as well as Britain's exit bill estimated at around 60 billion euros ($65 million).
Tusk also called for action to avoid a "hard border" between the Republic of Ireland and the British province of Northern Ireland.
A senior EU official said a key part of Saturday's summit would involve defining what "sufficient progress" means, with some states wanting to move on to the trade talks phase more quickly than others.
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Leaders will also discuss the relocation of two EU agencies currently based in Britain - the European Banking Authority and European Medicines Agency - which several EU states are bidding to host.
Tusk's comments come a day after a war of words between British premier May and German Chancellor Angela Merkel over the two years of negotiations.
Merkel said Britain should not have any "illusions" about getting favourable treatment. But May hit back by accusing the EU 27 of planning to "line up to oppose us".
EU officials have repeatedly stressed the 27's united front on the Brexit issue, after years of divisions over issues ranging from the euro to migration.
May "should not underestimate the commitment to unity," one European diplomat said.
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This was especially true on the sensitive issue of Britain's exit bill, the senior EU official said, adding: "I have never seen net payers and net contributors working so closely".
The leaders are also expected to back automatic membership for Northern Ireland after Brexit if it ever reunifies with Ireland, at Ireland's request, an EU Council source said.
"The European Council acknowledges that, in accordance with international law, the entire territory of such a united Ireland would thus be part of the European Union," says a clause in the draft summit minutes seen by AFP.
"This is speculation," a British government spokesman said when asked about the plan.
Britons voted to leave the EU in a closely-fought referendum in June 2016.
