Pregnant asylum seekers will give birth in Nauru for the first time since 2004 under the Abbott government's ''no exemptions'' approach to offshore detention.

Fairfax Media has learned a woman carrying twins is one of the first asylum seekers since the Howard era to face the prospect of giving birth in the tiny island republic.

Immigration Minister Scott Morrison Credit:Brendan Esposito

Refugee advocates are seeking details about the woman, who is said to be 22 weeks' pregnant and arrived on Nauru last Friday, according to sources on the island.

Of six pregnant women transferred from detention on Manus Island in Papua New Guinea by Labor earlier in the year, three miscarried.