On Tuesday, Italy recorded a drop in the number of people currently infected for the second day in a row.
By the end of this week Italy will announce a plan to gradually exit its lockdown, Prime Minister Giuseppe Conte said.
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 24,648 deaths, the highest recorded toll in Europe.
Data released on Tuesday showed the number of people currently confirmed as infected fell for the second consecutive day. But deaths rose by 534 in the previous 24 hours, compared with a rise of 454 announced on Monday.
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".
Current national quarantine restrictions officially expire on 3 May.
What about other European lockdowns?
Many European nations have slowly started to ease restrictions this week, with Germany, Austria, Denmark and the Czech Republic among countries allowing certain businesses to reopen.
There is however no co-ordination at an EU level, and countries are reopening at different rates.
Denmark was the first in Europe to allow pupils back in the classroom, with students under the age of 12 returning to education last week.
Norway allowed kindergarten students to return on Monday, provided they bring their own lunches and follow new hygiene rules.
But older students across Europe remain at home. France has officially extended its nationwide lockdown until 11 May, but even after then schools are not expected to return immediately.
Primary schools will likely return that week, followed by final year students from 18 May and all pupils from 25 May, the education minister Jean-Michel Blanquer said on Tuesday.
Spain has implemented one of the strictest lockdowns in Europe. Children of any age there are not currently allowed outside for any reason.
But the government announced on Tuesday that from 27 April children under the age of 14 would be able to accompany their parents on trips to grocery shops or pharmacies.
The lockdown itself meanwhile has been extended until 9 May. BBC