The Council of Europe meeting, at which Rishi Sunak will push for co-operation on tackling illegal migration, will not “have a big focus on migration”, host country Iceland has said.
The Prime Minister will warn European leaders in Reykjavik that the international system for policing human trafficking is “not working”.
He will also call for reforms to rules that prevented the UK’s first scheduled deportation flight taking asylum seekers to Rwanda.
She told BBC Radio 4’s World At One programme: “The biggest focus is of course Ukraine, and then other issues such as AI and environment and other things. So this summit doesn’t have a big focus on migration in general.
“But I agree that that is an issue for Europe. And of course, that system has to develop with the challenges that we face.”
Mr Sunak will hold talks with the president of the European Court of Human Rights (ECHR), Siofra O’Leary, over reforms to how Rule 39 works – the order that blocked the inaugural flight to Kigali last year.
Asked whether Iceland and other European nations will consider an overhaul of the rules, Ms Gylfadottir said: “I believe that there will be a discussion on it, but there will not be I think a real concrete outcome on reforming certain articles.”
His official spokesman told reporters: “I’m not going to pre-empt their discussion, but I imagine they will talk about Ukraine following president (Volodymyr) Zelensky’s visit to other countries and to see the Prime Minister yesterday.
“And I would have thought they will talk about the challenge of illegal migration.”
Northern Ireland would “potentially” be discussed as well, the spokesman said.
Mr Sunak is also expected to hold one-on-one talks with Mark Rutte, the prime minister of the Netherlands.
It comes as his Conservative administration attempts to pass into law measures designed to stop asylum seekers crossing the English Channel in small boats.
The Illegal Migration Bill aims to send asylum seekers who arrive in Britain via unauthorised routes back home or to a third country such as Rwanda, as well as cutting the daily £5.5 million cost of housing migrants who make it to the UK.
No 10 said the Government “remains committed” to reducing net migration amid speculation it could pass the one million mark next year.
It follows reports that the Home Office has privately shared figures with No 10 suggesting more than 1.1 million foreign workers and students could legally arrive in Britain in 2024/25, just as the Tories face a general election test.
Mr Sunak’s spokesman said: “I won’t get into specific pieces of advice that go between departments and No 10.
“The Government remains committed to reducing net migration over time while ensuring the economy has the skills we need.”
He said there is no specific target on reducing migration numbers and that the “priority is tackling illegal migration in the first instance”.
Cabinet minister Michael Gove, when it was put to him at the National Conservatism conference that net migration could hit the one million mark, said: “I don’t think it will reach those figures.”
But the Housing Secretary added that “the numbers recently have been at a level where there is an inevitable pressure on housing and on public services”.
The Leave campaigner said a “critical part of Brexit” was being able to “say this is the level of migration we as a country believe is right” and establishing that “there is a limit”.
Official figures to be released later this month are expected to show net migration of between 650,000 and 997,000 in 2022.
The 2019 Conservative Party manifesto pledged overall migrant numbers would “come down”.
Speaking ahead of his trip, the Prime Minister said: “It is very clear that our current international system is not working, and our communities and the world’s most vulnerable people are paying the price.
“We need to do more to co-operate across borders and across jurisdictions to end illegal migration and stop the boats.”
Home Secretary Suella Braverman argued in a speech at Monday’s National Conservatism conference that Britain “must not lose sight of the importance of controlling legal migration”, as well as preventing people from entering via unauthorised channels.
Tuesday’s gathering is only the fourth time the institution, which counts 46 countries as members, has met since its founding in 1949.
The meeting, which Ukrainian president Mr Zelensky is due to join virtually, will focus on the situation in his country and how international allies can hold Russia to account for breaches of international law since the invasion.
The Prime Minister will sign the UK up to the Register of Damages to ensure the people of Ukraine are compensated for the losses incurred as a result of the war, No 10 said.
The register is a mechanism to record and document evidence and claims of damage, loss or injury as a result of Russian aggression against Ukraine.
