Speaking in Northern Ireland on Tuesday, May vowed to seek a solution that keeps the border open and preserves the peace that ended years of violence in the British province.
He added he had agreed with Mr Tusk that "in light of the ongoing uncertainty in London and the fast-approaching deadline", preparations for a no-deal Brexit must intensify.
Irish premier Leo Varadkar has arrived in Brussels for talks with European Union leaders to discuss preparations for a no-deal Brexit.
They've been meeting to discuss Irish and European Union preparations in the event of a "no deal" scenario.
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"With the United Kingdom remaining a member of these deals throughout the transition period, we will then have the necessary time to focus on getting the trade deals that will lie at the heart of the UK's future prosperity right", he said.
The border area was a flashpoint during decades of conflict, and the free flow of people and goods across the frontier underpins the region's peace process.
"We expect that the backstop would never be used", Varadkar said.
At meetings in Belfast, May tried to tackle the biggest obstacle to getting a deal ratified by the British parliament - an insurance policy covering the possible future arrangements for the border between EU-member Ireland and the British province of Northern Ireland.
A day before British Prime Minister Theresa May - who is trying to chart a course that satisfies pro- Brexit hardliners in her party - is due in Brussels for talks, Tusk slammed those who made campaign promises that made the divorce seem easy.
British ministers, The Sun newspaper said, have been examining a plan drawn up by Japan's Fujitsu to track trade across the border, while the Telegraph said ministers had discussed delaying Brexit by eight weeks.
"I hope that tomorrow we will hear from Prime Minister May a realistic suggestion on how to end the impasse", he said. If the United Kingdom doesn't leave by then, the country would be under legal obligation to send MEPs to Strasbourg.