Spanish search teams were trawling the seabed for the body of a toddler off Tenerife Monday after investigators said they believed she -- like her sister -- had been killed by their father.

The case has shocked Spain, and on Monday crowds demonstrated at town halls across the country to protest domestic violence, following similar gatherings over the weekend.

The girls -- Anna, aged one, and six-year-old Olivia -- were reported missing on April 27 after being taken by their father, Tomas Gimeno.

On Thursday, the body of Olivia was found at the bottom of the sea off Tenerife wrapped in a bag weighted down with an anchor.

An autopsy carried out on Friday morning found Olivia had died a "violent death", the court said, after a gag order was lifted over the weekend.

The investigating magistrate in the case said it was "most likely" Gimeno had killed them both at home then dumped their bodies at a depth where they were unlikely to ever be found.

In a nine-page statement, the magistrate said that when Gimeno had taken the girls, he wanted "to kill them in a planned and premeditated manner".

"He aimed to inflict on his ex-partner the greatest pain that he could imagine, an inhuman pain," she said.

Witnesses have told investigators that on the day the girls went missing, Gimeno loaded several bags onto his boat.

Gimeno himself is missing and presumed to have committed suicide.

As search teams scoured the seabed, the magistrate leading the case said she feared both children had been killed
As search teams scoured the seabed, the magistrate leading the case said she feared both children had been killed AFP / DESIREE MARTIN

The case has gripped Spain, where 39 minors have been killed since 2013 by their fathers or by a partner or former partner of their mothers.

And so far this year alone, 18 women have been killed by their partner or ex-partner. Since officials began keeping records on January 1, 2003, the number of victims now stands at 1,096.

Spanish Prime Minister Pedro Sanchez said Friday "the whole of Spain is in shock" over the case.

A Tenerife court specialising in gender violence is now handling the case.

"Although only Olivia's body has been located so far the most probable hypothesis regarding Anna is, unfortunately, the same," the magistrate there said.

The suspected abduction and murder of the two girls came a year after the girls' mother, Beatriz Zimmermann, broke up with Gimeno.

He sent her "offensive and insulting" messages following the break-up, especially after she found a new partner, the magistrate said.

"The defendant's desire was to leave his ex-partner in the dark as to the fate of Olivia and Anna," she wrote.

In an open letter published on Sunday, the girls' mother wrote that it was "the most monstrous act a person can commit: killing their own innocent children".

"When they told me the news, the world came crashing down on me, and as hard as it is, at least now I can mourn their loss," she wrote.

"I wish I had been there at that moment holding their hands so we could die together... But that couldn't be, because Tomas wanted me to suffer searching endlessly for them all my life."