Conte said he had spent the day in contact with his 27 EU peers, reminding them that they had agreed at their end-June summit on the need to share the burden of dealing with the migrant influx.
In a letter addressed to European Commission head Jean-Claude Juncker and EU President Donald Tusk, Conte demanded others should help and not leave Italy in the lurch.
"In this context which always sees Italy in the frontline of saving lives at sea, I ask you for a clear sign on sharing the responsibility of managing the migrant issue and to envisage the possibility of a port taking in, or to take charge of some of the 450 migrants picked up," he said.
There was no immediate confirmation from the French.
The migrants, like thousands of others, had set sail from Libya in a single wooden vessel which was identified early Friday while passing through waters under Malta's jurisdiction.
But Italy's far-right Interior Minister Matteo Salvini, who has authority over the country's ports, on Friday refused to let them dock in the latest demonstration of his no-go stance on accepting more migrants.
Silvini insisted instead that the two Frontex vessels be instructed to "head south, to Libya or Malta".
"We need an act of justice, of respect and of courage to fight against these human traffickers and generate a European intervention," he said in talks with Conte, according to reports carried by Italian news agencies.
Cited by the Italian media, cabinet sources said Conte was going to push for them to be immediately transferred to other European countries, otherwise they would not be allowed to land.
In an exchange of messages, emails and phone calls on Friday, Rome had pushed Valletta to take responsibility for those on board the wooden boat.
But Malta said the ship was much closer to the Italian island of Lampedusa, and yesterday, insisted it had respected "all of its obligations under international conventions" concerning those rescued at sea.
Last morning, as the two Frontex vessels approached the boat, several migrants threw themselves overboard, prompting immediate efforts to rescue them from the water, Italian sources said.
Eight women and children were taken to Lampedusa for medical treatment. The latest standoff came just hours after 67 migrants were allowed to disembark from an Italian coast guard ship in Sicily late on Thursday.
Salvini, who took office when Italy's new populist government came to power on June 1, wants to block any further migrant arrivals by boat and has banned NGO rescue ships from docking in Italian ports, accusing them of aiding human traffickers.
Last month, the French rescue ship Aquarius and the German boat Lifeline, who between them were carrying hundreds of migrants, were forced to divert to Spain and Malta respectively after Italy turned them away.
Italy, Greece and Spain have been on the front line of the migrant crisis, with Europe deeply divided over how to share the burden of the massive influx of people seeking a new life in Europe.
Separately, Spanish rescuers saved more than 340 migrants in the Mediterranean yesterday.
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