European Council President Donald Tusk, right, next to European Commission President Jean-Claude Juncker | Pool photo by Ng Han Guan via Getty Images Donald Tusk: Post-Brexit deal should be ‘as special as possible’ European Council president says EU is offering far-reaching deal on trade, internal security and foreign policy.

The EU wants a relationship with the U.K. after Brexit that is "as close and special as possible," said European Council President Donald Tusk, stressing that a far-reaching deal on trade and security is still on the table.

In a statement delivered alongside Leo Varadkar, the Irish prime minister, following their meeting in Brussels Thursday, Tusk again stressed the backing of the rest of the EU for Ireland on the border question. But despite the entrenched positions of London and Brussels in the talks, Tusk stuck firmly to the EU's offer, giving no hint of movement or compromise.

Tusk's rejection of the U.K.'s Brexit plan at an EU leaders' summit in Salzburg, Austria last month prompted an angry reaction from Prime Minister Theresa May. She underlined her position Wednesday by insisting in her speech to the Conservative Party's conference that what the EU is offering is not acceptable.

“From the very beginning, the EU offer has been not just a Canada deal, but a 'Canada plus plus plus' deal. Much further-reaching on trade, on internal security and on foreign policy cooperation. This is a true measure of respect. And this offer remains in place,” said Tusk in a prepared statement.

May has explicitly ruled out having Northern Ireland within the EU's customs territory.

By "Canada plus plus plus," Tusk is referring to a souped-up free-trade agreement — like the one that the EU has with Canada but with add-ons. However, such an arrangement would require Northern Ireland to remain within the bloc's customs territory and subject to some EU regulations to avoid the need for customs checks at the border with the Republic of Ireland.

May has explicitly ruled out having Northern Ireland within the EU's customs territory because that would mean an economic barrier between it and mainland Britain. In her conference speech, she called the EU's Canada offer, "a deal that carves off Northern Ireland, a part of this country, effectively leaving it in the EU’s custom’s union ... we will never break up our country."

Brexiteers also sometimes advocate a "Canada plus plus plus" deal with the U.K. outside of the EU’s customs union, able to exercise an independent trade policy and strike bilateral trade deals with non-EU countries. They argue that a hard Northern Ireland-Republic of Ireland border could be avoided using technological solutions. May insisted in her conference speech that “no simple free-trade agreement” could avoid a hard border, “not even one that makes use of the very latest technology.”

Tusk stressed that the EU would not abandon Dublin for the sake of reaching a deal: “The EU is united behind Ireland and the need to preserve the Northern Ireland peace process.”

He said negotiators are working to find a format for a so-called backstop that will achieve the aim of avoiding north-south border checks, but at the same time be acceptable to London. “Despite the U.K. government's rejection of the original EU backstop proposal, we will not give up seeking a workable solution that fully respects the Good Friday Agreement as well as the integrity of the single market and the customs union,” he said.

Varadkar, who also met with EU Brexit negotiator Michel Barnier and the Parliament's Brexit coordinator Guy Verhofstadt, thanked "the European Council and all the European institutions for their ongoing solidarity with Ireland as we enter what is going to be, I believe, a critical and ultimate phase in negotiations.”

He said that Dublin's priorities in the talks include avoiding a hard border and protecting the rights of citizens in Northern Ireland “who will continue to be Irish and therefore European citizens.”

Diplomats say they expect an amended British proposal on the Ireland backstop soon, ahead of a European Council summit on October 17-18.

But one EU official said they expect the U.K. to be cautious about formally submitting a proposal that might meet with immediate rejection and potentially inflame the tensions between the two sides. “This time it seems that London wants first to test the water, to see whether it will fly before putting it officially on the table,” said the official.

Charlie Cooper contributed reporting.