Greece wants EU border agency Frontex to operate beyond Europe’s waters to stop illegal migrants.
Notis Mitarachi, migration minister for Greece, made the proposal at a meeting with his EU counterparts in Portugal on Tuesday.
Currently, Frontex's operational area extends to Greece's sea borders with Turkey. The agency faces controversy over its alleged role in migrant "pushbacks" at sea, which it denies.
Mr Mitarachi said Frontex could expand its operations to non-EU countries.
“For Greece, the fight against irregular migration is a top priority,” he said.
“In this regard, we proposed the activation of Frontex outside the territorial waters of Europe, so that they can effectively stop the movement of illegal immigrants.”
Frontex has about 600 officers in Greece monitoring the border and dealing with incoming migrants.
The agency's Operation Poseidon also deals with weapons smuggling and illegal fishing.
More than a million refugees and migrants entered Greece at the height of the 2015 refugee crisis, mostly on boats from Turkey.
Numbers have dropped, especially during the pandemic, but tensions with Ankara rose last year after Turkish authorities flung open the land border to thousands of migrants.
Greece closed its north-eastern land border in response and tightened patrols at sea with the help of Frontex.
Both face accusations of forcing back migrants from Turkey seeking asylum.
Greece under pressure over alleged migrant pushbacks
Europe’s top human rights body expressed “deep concern” at the persistent allegations against Greece in a letter made public on Wednesday.
Dunja Mijatovic, the Council of Europe Commissioner for Human Rights, urged the Greek government to “put an end to these practices and to ensure that independent and effective investigations are carried out”.
In a letter addressed to three Greek ministers, she said Greece could no longer "simply dismiss allegations of pushbacks despite the overwhelming body of evidence".
She said there had been an increase in reported cases of migrants being taken on life rafts by Greek officers and pushed back to Turkish waters.
Athens denies the claims and said the allegations were “largely unsubstantiated”.
At Frontex, an internal report in March cleared the agency of wrongdoing in eight of 13 reported cases of pushbacks, but five were unresolved.
Human Rights Watch said the inquiry failed to look at "scores of other incidents" of alleged pushbacks.
An internal investigation identified deficiencies at Frontex and called for a new culture aimed at detecting possible misconduct.
A new strategy unveiled by the European Commission last month put Frontex at the centre of plans to deport more migrants. Key to the Commission's strategy is persuading migrants to return voluntarily, in order to reduce the cost of deportations.
The European Parliament’s research service estimated it costs €3,414 ($4,120) to deport someone forcibly, compared with about €560 if they go voluntarily.
Some migrants received free flights, small payments and other incentives to leave.
