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A Melbourne man who claimed his missing wife might have been abducted by Muslim extremists has admitted he killed her, a court has been told.

Nasir Ahmadi, 46, faced an out-of-sessions court hearing on Friday night charged with the murder of Zahara Rahimzadegan.

"I love my wife," he told the hearing.

"But she's dead."

Detective Senior Sergeant Ron Iddles told the court that a woman's body was found buried underneath a concrete pad and a newly-constructed timber deck in the backyard of the couple's Ashwood home.

"He has made full admissions in relation to this offence," he told the hearing.

Ahmadi had previously claimed that his 46-year-old wife, also known as Mandy Ahmadi or Glorious, could have been a target of extremists for converting Muslims to Christianity.

But homicide detectives gave no weight to the theory and a day after taking on the case entered the couple's home on Friday morning armed with a search warrant and rakes and shovels.

Det Sen Sgt Iddles said Ahmadi was arrested in the morning and interviewed throughout Friday.

By late afternoon police had ripped up the deck at the property, in Melbourne's southeastern suburbs, and unearthed the remains, which police believe are those of his missing wife.

Ahmadi had reported Zahara missing two days after she vanished on December 16 last year.

The couple came to Australia with... >>>