Investigators said drug traffickers lured the young women into a van on September 19, the trio thinking they were going to a party.
According to several Argentine media outlets, the women had been asked to attend a party as sex workers.
A cousin of Brenda and Morena told AFP the pair had sometimes engaged in sex work “to survive”, without their families’ knowledge.
The killings caused widespread shock among the public in Argentina, with thousands of people demonstrating last weekend to demand justice.
Valverde is suspected of running a drug gang in the Zavaleta neighbourhood of Buenos Aires.
His lawyer, Marcos Sandoval, has maintained his client’s innocence and claimed his work in Argentina involved harvesting blueberries and selling socks.
Valverde was arrested on Wednesday with a suspected Argentine accomplice, 28-year-old Matias Ozorio, in the southern Lima district of Pucusana.
On Wednesday, Ozorio was deported to his homeland.
In Argentina, seven people have been arrested over the murders.
– Agence France-Presse