Downing Street has hinted that it still hopes to secure agreement on parallel Brexit talks, despite senior European leaders rejecting the plan.
However, German chancellor Angela Merkel and French president Francois Hollande have both stated their opposition, arguing that the UK must complete divorce talks first.
Brexit secretary David Davis has already pushed back, and today a spokesman for May hinted that Downing Street is still hoping to reach agreement.
"We are at the beginning of a negotiation and we would expect people to take robust positions at the beginning," he said.
"The government's position remains as it as yesterday. We believe that this negotiation should take place in parallel."
May's letter to Tusk had suggested that the government viewed simultaneous talks as critical to meeting the 2019 deadline stipulated by Article 50.
"We recognise that it will be a challenge to reach such a comprehensive agreement within the two -yar period set out for withdrawal discussions in the Treaty. But we believe it is necessary ot agree the terms of our future partnership alongside those of our withdrawal from the EU," May wrote.
"We start from a unique position in these discussions - close regulatory alignment, trust in one another's institutions, and a spirit of cooperation stretching back decades. It is for these reasons, and because the future partnership between the UK and the EU is of such importance to both side, that I am sure it can be agreed in the time period set out by the Treaty."