The Tory leader wants to agree a plan with Corbyn to get a Brexit deal through Commons.
Tusk sent the tweet sent soon after May spoke at her Downing Street office.
British Prime Minister plans to seek an extension to the deadline for Britain's departure from the European Union, as she reaches out to opposition politicians to help resolve the Brexit impasse.
"We will meet the Prime Minister", he said. "To be clear, during any long extension there will be no renegotiation of the Brexit withdrawal agreement, no, never", he said.
The UK leaving without an agreement is considered the worst-case scenario due to its debilitating impact on the economy, besides disrupting rules and regulations affecting every aspect of everyday life developed and implemented over 40 years of the UK's membership of the EU.
Ford's European boss said that if the United Kingdom can't work out a deal on leaving the EU that guarantees "frictionless trade", the vehicle maker "will have to consider seriously the long-term future of our investments in the country". "The British Parliament has said itself that it doesn't want a disorderly Brexit".
May has summoned her Cabinet for a marathon meeting Tuesday to thrash out the options.
"We will need a further extension of Article 50, one that is as short as possible and which ends when we pass a deal", she said.
May said she was seeking a single, unified approach.
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Almost three years since the United Kingdom voted to leave the EU in a shock referendum result, British politics is in crisis and it is unclear how, when or if it will ever leave the European club it first joined in 1973.
The April 12 deadline, imposed by the European Union, gives May less than two weeks to bridge the hostile divide that separates those in her government who want to sever links with the European Union and those who want to keep the ties that have bound Britain to the bloc for nearly 50 years.
Fearful that her refusal to change course is putting Britain at risk of a "no-deal" exit, pro-European MPs last week seized the initiative by holding a round of votes on eight alternative options.
"Over the last days a no-deal scenario has become more likely, but we can still hope to avoid it", European Union chief Brexit negotiator Michel Barnier said in Brussels.
They had been hoping to pass a law to force a soft Brexit option on Theresa May, but after disastrous indicative votes last night ended in stalemate they will instead try to force through a bill compelling the PM to ask for a long delay at an European Union summit on April 10.
On Wednesday French President Emmanuel Macron emerged from a meeting with Irish Prime Minister Leo Varadkar to say that the EU's consent to a Brexit delay should not be taken for granted. The focus will be again on whether May can secure a majority for another round of votes on her deal later this week, so expect the pound to react to news on that front.
Hinds tells the BBC that the deal "is a good balance, and I hope colleagues can get behind it".
"The sensible way forward, and I think the one PM would take if this was a serious attempt to build consensus, is to agree to fight an election, seek a longer delay and allow the option of a public vote on what the Commons agrees to", Ms Sturgeon said.
Despite the downbeat assessment, Barnier did say that "we can still hope to avoid it" through intensive work in London ahead of an April 10 summit.