Cambodia says it has agreed to take its first batch of migrants from Australian custody as part of a controversial deal between the countries that prompted widespread international criticism.

Four migrants held by Australia on the remote Pacific island of Nauru will soon be transferred to the Southeast Asian nation, Cambodia's interior ministry said on Thursday.

"The four refugees have filled in the voluntary applications," Khieu Sopheak, a spokesperson for the ministry, told AFP news agency.

"Then the Ministry of Interior asked the government to have the four refugees resettle permanently in Cambodia and the head of the government [Prime Minister Hun Sen] approved this request yesterday," he said.

The migrants include a Rohingya man from Myanmar, two Iranian men and one Iranian woman, all of whom were granted refugee status on Nauru and had agreed to be moved, Khieu Sopheak said.

No date has been set for their arrival.

Under Australia's immigration policy, migrants who arrive by boat are denied resettlement in the country and sent to Papua New Guinea and Nauru, even if they are genuine refugees.

Australia signed a deal with Phnom Penh in September to allow those granted refugee status in Nauru to permanently resettle in Cambodia, one of the poorest nations in Southeast Asia.

The UN condemned the deal, while refugee advocates said the migrants did not want to be sent to Cambodia.

Cambodia has also been criticised for its own record of helping migrants, including Vietnamese Montagnards who are often deported.

The mainly Christian ethnic minorities in Vietnam's mountainous Central Highlands have crossed the border to Cambodia in recent years to escape discrimination.

Source: Agencies