"I was exasperated - they kept asking me for more and more money," Raj, 35, told police during questioning, as cited on Monday by Latina Oggi newspaper.
He was arrested on Sunday in nearby Aprilia on suspicion of murdering the two women after police bugged his phone.
Di Grazia was found dead in the kitchen of her home with a single stab wound to her neck, while her daughter from a previous marriage was stabbed four times in the neck in her bedroom.
Raj wed Di Grazia in Kurukshetra in Haryana in December 2008 in what appears to have been a marriage of convenience.
As Di Grazia's husband, Raj obtained Italian citizenship and agreed to pay her 8,000 euros in instalments of 150 euros.
But Di Grazia had recently been nagging him for ever-bigger chunks of the cash, according to Raj.
Raj comes from the village of Ram Saran Majra in Haryana and worked in Italy as a manual labourer on building sites.