The Prime Minister and the president of the European Commission both underlined a “shared interest” in tackling cross-border crime and people trafficking during a bilateral talk at a Council of Europe summit in Iceland, according to No 10.
The arrangement would see British agencies working together with Frontex, the EU border force, on “critical operational and strategic challenges including the situation in the Channel”, a Downing Street spokesman said.
The UK and the EU will now discuss “the details and operationalisation of this new working arrangement”, they added.
Mr Sunak had sought to make migration a key topic at the summit in Reykjavik on Tuesday, warning leaders that the international system for policing human trafficking is “not working”.
He also called for reforms to Strasbourg measures which have hampered his Rwanda plan.
Mr Sunak held talks with the president of the European Court of Human Rights (ECHR), Siofra O’Leary, over a review of how Rule 39 works – the order that blocked the inaugural flight to Kigali last year.
People trafficking came up in the Prime Minister’s bilateral meeting with Dutch leader Mark Rutte, with whom he agreed to “tackle the scourge” by working together “both bilaterally and through forums such as the European Political Community”, according to Downing Street.
At the summit, Mr Sunak said that both European communities and the world’s most vulnerable are “paying the price” for the failure to prevent unlawful migration.
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.
The Council of Europe was established following the Second World War to uphold democracy and freedom throughout the continent.
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 Volodymyr 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.