The Italian prime minister's comments come after far-right Interior Minister Matteo Salvini announced plans for a Roma census. Salvini defended the census and tried to shift the focus to the protection of Roma children.
Conte also called for checks to ensure Roma children had access to school services, as "they are often kept out of compulsory education courses."
Salvini, who also serves as deputy prime minister, announced his intentions of carrying out a Roma census during a television question-and-answer session on regional television channel TeleLombardia on Monday.
The far-right League party leader said the census would mean Roma who were in the country illegally could be deported, but "as for the Italian Roma, unfortunately, one has to keep them at home."
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Salvini defends census plans
Following criticism from Conte and a number of opposition MPs who labelled the register "racist" and "fascist," Salvini defended his proposal.
"I'm not giving up and I'm pushing ahead! The Italians and their safety first," Salvini tweeted.
Fellow Deputy Prime Minister Luigi Di Maio, who is the leader of the anti-establishment Five Star Movement that makes up the coalition alongside Salvini's League, also said any census based on ethnicity would be "unconstitutional."
Salvini's move also drew condemnation from opposition MPs, including members of Italian opposition center-left Democratic Party (PD).
"Yesterday refugees, today the Roma, tomorrow guns for everyone. It must be tiring being nasty," former premier Paolo Gentiloni tweeted on Monday.
The PD's current leader Matteo Orfini tweeted: "If we really want to carry out the census, I would start with the census of racists and fascists. To better avoid them."