The talks are due to formally begin next March, but Tusk said the position being adopted by some British MPs "has nothing to do with reality."
His comments, to a group of UK parliamentarians, represent a stinging rebuke to those pushing for the UK to remain in the single market without accepting free movement of people, one of the four basic and founding principles of the EU.
Tusk was responding to a letter from 81 British MPs and peers calling for reciprocal rights for EU and UK citizens to be agreed at the next EU summit in December.
Some British government ministers are pushing Theresa May's government to adopt an immigration system with restrictions on both skilled and unskilled workers.
But in his response to the MPs, Tusk said, "In your letter you state that the European Commission, and in particular its lead Brexit negotiator Michel Barnier, are attempting to prevent negotiations, thereby creating 'anxiety and uncertainty for the UK and EU citizens living in one another's territories.'
"It is a very interesting argument, the only problem being that it has nothing to do with reality. Would you not agree that the only source of anxiety and uncertainty is rather the decision on Brexit?"
He added, "In your letter, you called on me 'to resolve this matter once and for all' at the European Council in December. This would in effect mean the start of the negotiations already in December. The EU stands ready to do so, but that can only happen on the condition that article 50 has been triggered."
Tusk adds, "Let me reiterate, however, that the decision about triggering article 50 belongs only to the UK, which we fully respect."
Further comment came from Liberal Democrat leader Tim Farron, who said that the UK government was heading towards a hard Brexit if it was unwilling to maintain an open system.
"Cracking down on skilled workers will hurt our economy. What makes Britain best is when we are open, tolerant and looking towards the world," he said.
Meanwhile, commenting on leaked papers on the government's Brexit negotiations, Keir Starmer, the shadow minister for Leaving the EU, said, "The case for government to come clean, to end this unnecessary uncertainty and publish a clear plan for Brexit is now overwhelming.
"Two weeks ago Boris Johnson told a Czech newspaper that the government is not planning for the UK to stay in the customs union, yesterday we learn from leaked notes that the government does not intend to stay in the single market either.
"These disclosures are significant because they suggest that the government is not even going to fight for the single market or customs union in the negotiations. If that is the case, there are huge implications for the economy, for businesses and for jobs in the UK."