Italy's Prime Minister Giuseppe Conte speaks during a press conference held at Rome's Chigi Palace, following the Ministers cabinet meeting dedicated to the corinavirus crisis, on March 4, 2020. (Photo: AFP)

Italy banned domestic travel and shut down a range of industries on Monday in a last-ditch push against the spread of a coronavirus that has killed nearly 5,500 people in a month.

The wave of restrictions is designed to ensure Italy gets through a 10-day stretch in which the rate of deaths and infections is supposed to finally drop.

"Everyone's effort is needed," Prime Minister Giuseppe Conte told reporters.

"The country's social and economic strength is at stake."

Italian health officials reported that the rate of increase in both deaths and declared infections slowed on Sunday -- albeit from a high base.

There were 651 fatalities on Sunday compared with Saturday's record 793 deaths while the number of new reported infections fell to 5,560 from 6,557.

But Conte told Italians it was too early to let down their guard.

"We have not reached the most acute phase of the infection and the numbers will continue to grow," he said.

"Much depends on the responsible behaviour of each one of us."

Conte's latest order comes after he caused confusion on Saturday by ordering all "non-essential" factories and trades to shut until April 3. 

The government released a long list of industries and professions that would still be allowed -- including translation services and computer repair shops.

Auto part makers were allowed to stay open but steel mills were shut. News stands were allowed to stay open but book stores were not.

Italians frustrated with the ever-changing regulations began to parody officials on social media who had released video messages threatening to jail joggers and fine people walking their dogs too far from their house.

The decrees published on Monday added to an air of confusion in the face of a disease Conte has called Italy's biggest threat since World War II.

They include a separate instruction forbidding Italians "from moving by public or private means of transport outside the municipality in which they are currently located".

There is an exception for people who can prove they must travel "for work needs of absolute urgency or for health reasons".

The reality is that Conte's team is running out of things to close or ban.

Ministers and health experts are all looking at the daily death toll and infection rates to see if their approach has worked.

They pleaded with Italians to sacrifice individual liberties for the common good for two weeks.

The initial restrictions placed on Lombardy -- the northern region at the centre of the Italian epidemic that includes the financial capital Milan --  expired on Sunday and the national measures are set to end on Wednesday.

Conte indicated last week that he might need to extend the restrictions indefinitely.

His decision is expected this week.

"If everyone -- and I stress everyone -- respects our bans, we will emerge from this very difficult test first," Conte said on Monday.