In a Facebook post, Mr Conte said the country could not give up its policy of “maximum caution”, and said Italy would reopen in line with “serious scientific policy”.
“A reasonable expectation is that we will apply it from May 4,” he said.
Italy has reported 24,114 deaths, the highest recorded toll in Europe.
Data released on Monday showed the number of people officially confirmed as infected with coronavirus had dropped for the first time since the outbreak began. Italian authorities said the symbolic drop of 20 cases was a “positive development”.
The third-largest economy in the eurozone has been under lockdown measures since 9 March, brought in to tackle the spread of the virus.
Countries across Europe are slowly beginning to ease the restrictions, on businesses and on education. There is however no co-ordination between states.
Some countries like Denmark have already reopened primary schools, while Spain’s government on Tuesday finally decided to allow children outside – under strict conditions.
What did Italy’s PM say?
Mr Conte posted his statement on Facebook on Tuesday morning, insisting the government was working non-stop to co-ordinate moves towards “phase two” of its lockdown – “coexistence” with the virus.
“I would like to be able to say, let’s open everything. Right away,” he wrote. “But such a decision would be irresponsible. It would make the contagion curve rise uncontrollably and would jeopardise all the efforts that we’ve made until now.”
“The easing of measures must take place on the basis of a well-structured and articulated plan,” he said, adding that Italy “cannot abandon the line of maximum caution”.