LONDON - British Prime Minister Rishi Sunak said he was "giving it everything" to strike a new post-Brexit deal with the European Union on Northern Ireland's trade arrangements, calling it vital to ensuring a return to power-sharing in the province.

"There's unfinished business on Brexit and I want to get the job done," Sunak told The Sunday Times newspaper, which said the announcement of a deal was expected as soon as Monday.

That is when lawmakers in Sunak's Conservative Party have been told to be in parliament.

As part of its 2020 agreement for leaving the EU, Britain reached an accord with Brussels known as the Northern Ireland Protocol to avoid imposing politically contentious checks along the 500 kilometre (300 mile) land border with EU member Ireland.

But the protocol effectively created a border in the Irish Sea for some goods moving from Britain because it kept Northern Ireland in the European Union's single market for goods.

Sunak said he would try to resolve the concerns about the deal expressed by the Democratic Unionist Party (DUP), which is worried about the EU retaining influence over Northern Ireland.

Ireland's prime minister Leo Varadkar told reporters earlier on Saturday that Britain and the EU were inching forwards.

Sunak said he was hopeful of a positive outcome to the talks and he would spend the weekend trying to finish them.

In a nod to the DUP, he said the 1998 Good Friday peace deal for Northern Ireland had been unbalanced by the protocol, which has prompted the DUP to boycott Northern Ireland's assembly.

"If we want to restore the power-sharing institutions in Northern Ireland, which I very much want to do and I think that's what people need and deserve, then we need to resolve the issues of the protocol," Sunak said.

He said Wednesday's shooting of a police officer "reminds us of the delicate situation in Northern Ireland, the fragility of it, and we shouldn’t take it for granted. And that’s why getting power-sharing up and running is really important."

The officer is in critical condition in hospital.

The Sunday Times said Sunak was confident the deal met all the DUP's conditions but the party was unhappy that Northern Ireland would have to apply some EU single-market legislation, unlike the rest of the United Kingdom.

The DUP's leader Jeffrey Donaldson was "minded to reject the deal," the newspaper said.

Asked about anger among DUP and some Conservative lawmakers - including former prime minister Boris Johnson - over being kept in the dark about the deal, Sunak said: "I know, people will always want to know every single detail, but ultimately you can't conduct a very complicated negotiation in public."

(Writing by William Schomberg; Editing by Alexander Smith)