The justice minister of Cyprus has resigned over the case of a serial killer who has confessed to killing seven foreign women and girls amid mounting reports police had bungled their investigation when some of the victims were initially reported missing.

A Cypriot army captain has admitted to killing seven foreign women and girls as police continue the search for the bodies of three of the victims.

Justice Minister Ionas Nicolaou said he was stepping down as a matter of "conscience and principle" because the killings that authorities have described as "unprecedented" have deeply shaken the east Mediterranean island nation of just over a million people.

But he said he bore no responsibility in how police handled the missing persons' reports, and law enforcement authorities never informed him about them.

Nicolaou said it was "completely unfair" to apportion blame either to himself or the government for any investigative lapses in the missing persons' reports because a minister "doesn't get involved nor should he get involved" in such investigations.

Among the reasons that led to his resignation was the repercussions of the killings extend beyond the police and touch society's own "attitudes and perceptions that honour none of us."

Victims originally from Philippines, Romania

He urged the public to continue showing trust in the police force and said he would ask the police complaints commission to proceed with its own independent probe into the police handling of the case.

"We've all gone through difficult days because of this unprecedented case. It's human," Nicolaou said, reading from the written statement after a two-hour meeting with Cyprus President Nicos Anastasiades.

Members of the Cyprus Special Disaster Response Unit search for a suitcase in a manmade lake on Monday near the village of Mitsero outside of the capital of Nicosia as part of the investigation. (Petros Karadjias/Associated Press)

Anastasiades said he accepted Nicolaou's resignation with "deep regret" because he would miss the services of one of his closest collaborators, praising his "political ethos."

Anastasiades repeated he shares the public's shock and revulsion over the killings.

"I want to assure of the government's determination to solve these abhorrent murders and also these actions or omissions regarding missing persons reports," he said in a written statement.

Police spokesperson Andreas Angelides said the police chief has ordered a second, separate investigation into the disappearances of three of the victims who vanished in September 2016 and December 2017.

Angelides said both probes aim to uncover whether police followed proper procedures or mistakes were made that constitute "either disciplinary or criminal acts." Their findings will be forwarded to the attorney general.

Only 1 victim ID'd

Only one victim, Mary Rose Tiburcio, 38, from the Philippines, has been positively identified in the case so far. Her bound body was discovered April 14 down an abandoned mineshaft.

A second body, believed by police to be Arian Palanas Lozano, 28, also from the Philippines, was found in the mine shaft six days later.

Authorities are separately searching a reservoir for the body of Tiburcio's six-year-old daughter Sierra.

On Sunday, divers pulled a suitcase containing the badly decomposed body of a woman out of a toxic lake that is part of a disused copper mine. Crews are searching for two more suitcases.

The victims in the lake are believed to be Maricar Valtez Arquiola, 31, from the Philippines; Florentina Bunea, 36, from Romania; and Bunea's eight-year-old daughter, Elena Natalia.

Arquiola has been missing since December 2017. The Romanian mother and daughter vanished in September 2016.