The prime minister addressed the Senate ahead of two parliamentary confidence votes expected to confirm his new cabinet, formed from a coalition of far-right and eurosceptic parties.
His government was sworn in on Friday after almost three months of political turmoil that alarmed EU officials and spooked financial markets.
A lawyer with little political and no government experience, Conte was nominated by far-right League leader Matteo Salvini and the head of the anti-establishment Five Star Movement (M5S) Luigi Di Maio – both of whom are now his deputy prime ministers.
Conte's maiden policy speech reaffirmed several of the coalition's key manifesto themes, including a tough line on migrants, rejection of economic austerity and conciliatory gestures towards Moscow.
"We want to reduce our public debt, but we want to do so with growth and not with austerity measures," he told senators.
"We will strongly call for the Dublin Regulation to be overhauled in order to obtain respect for a fair distribution of responsibilities and to achieve an automatic system of compulsory distribution of asylum seekers."
On Russia, which faces EU sanctions over the Ukraine crisis, Conte said: "We will promote a review of the sanctions system."
Summits on horizon
Both former premier Silvio Berlusconi's Forza Italia party – a campaign ally of the League – and the outgoing centre-left Democratic Party have said they will not vote in favour of the new government.
But the alliance between the anti-establishment M5S and far-right League is expected to pass the confidence votes in the Senate on Tuesday and in the lower Chamber of Deputies on Wednesday as the two parties hold a majority in both houses.
On the 53-year-old prime minister's agenda in his first weeks in office are a Group of Seven summit in Canada this week and a key EU summit at the end of the month.
Conte's low profile has fuelled speculation that he will take a back seat to his two powerful deputies.
Salvini is to be interior minister in the new cabinet and Di Maio will hold the economic development portfolio.
"Good times over"
On Monday, Di Maio met representatives of food deliverers in Italy's gig economy.
Afterwards Di Maio described the workers as "the symbol of an abandoned generation", and underlined the need to give them "job security and a dignified minimum wage".
Salvini has wasted no time addressing immigration.
Visiting Sicily, where thousands of migrants have arrived in recent years, he declared at the weekend that Italy "cannot be Europe's refugee camp".
The 45-year-old has repeatedly promised to cut arrivals and accelerate expulsions from a country where around 700,000 migrants have arrived since 2013.
"The good times for illegals are over – get ready to pack your bags," he said on Saturday.
European Union interior ministers are meeting on Tuesday to discuss possible reforms of the bloc's controversial Dublin regulation, whereby refugees must file for asylum in the first member state they enter.
Salvini has blasted the regulation as unfairly burdening Mediterranean countries and leading to "an obvious imbalance in management, numbers and costs".
He and Di Maio have been heavily criticised for remaining silent on the murder of Soumaila Sacko, a 29-year-old Malian who died from gunshot wounds after an unknown assailant fired at him and two others on Saturday.
However, on Tuesday Conte called the incident "tragic and troubling", adding that Sacko was "one of thousands of day labourers with correct immigration papers who every day in this country go to work in conditions below any level of dignity".
He added: "Politics should bear the responsibility of these peoples' ordeals and ensure pathways of legality, which is the guiding light of our government program."