Prime Minister Giuseppe Conte came under attack on Monday from Italy's Catholic bishops and even some of his own cabinet members for refusing to reintroduce mass once the coronavirus lockdown is lifted.

Conte has unveiled a gradual easing of restrictions that will restore some semblance of former life starting on May 4.

The Mediterranean country's official death toll of 26,664 is Europe's highest and second globally only to the United States.

But the number of infections has been ebbing and scientists believe the contagion rate is low enough to gradually get back to work.

Conte has allowed Italians to take strolls in parks and go jogging starting next Monday.

More stores will reopen and restaurants will resume takeout service.

Even museums will unlock their gates on May 18 in an effort to draw back tourists and help out Italy's devastated hotel and services industry.

But there will still be no mass and attendance at funerals will be limited to 15 people.

Conte and Health Minister Roberto Speranza agreed with a scientific committee conclusion that "the elderly in the parish are too frail to risk", La Repubblica daily wrote.

The bishops are livid.

"We cannot accept to see the freedom of worship compromised," the Italian Episcopal Conference of the country's top bishops said in a statement.

"Why on earth, with proper precautions, can you go to a museum but not to mass?"

The Corriere della Sera newspaper said the bishops had been lobbying Conte to allow Sunday mass services that would be limited to about 20 people.

They also urged up to 15 people to permitted to attend weddings and baptisms -- currently also restricted to just the pastor and immediate family members.

But Conte only allowed broader access to funerals and promised to look into how other religious curbs can be relaxed in the coming weeks.

"I understand that freedom of worship is a fundamental people's right," Conte told the nation on Sunday.

"I understand your suffering. But we must continue discussing this further with the scientific committee."

Italy's Family Minister Elena Bonetti called Conte's decision "incomprehensible".

"It is up to politicians to protect the country's wellbeing, and religious freedom is among our fundamental rights," the minister said.

La Repubblica daily warned that Conte was developing powerful enemies at a critical juncture.

Italy's competing political forces had appeared to put aside their squabbles as the nation entered what was widely regarded as its gravest emergency since World War II.

But Conte has been coming under growing criticism and pressure from regional leaders and political opponents as he decides which industries to open up first.

"This is the (bishops') first open conflict with the prime minister," La Repubblica noted.

"There is a battle being waged over everything."