The Mediterranean country's toll reached 3,405 after it recorded 427 new deaths on Wednesday.
The United States is urging Americans not to travel abroad at all and could announce restrictions at the U.S.-Mexican border on Friday
The number of infections has reached 24,747, a count released to the media by Italy's civil protection service said.
Under a government decree issued earlier in the week, people had been allowed to walk, jog or bike in parks as long as they kept at least a distance of 1 meter between each other.
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Italians have been told to avoid all non-essential travel as quarantine measures were extended to the whole country to stop the spread of Coronavirus
The restrictions will take effect on Tuesday and like those in northern Italy will last until April 3, Giuseppe Conte said
The number of fatalities nearly tripled, rising from 133 to 366 Sunday, according to the civil protection agency, with most deaths occurring in the hard-hit Lombardy region in Italy's wealthy north.
The Kerala government has said that it is strengthening preventive measures in the wake of the fresh cases
Italy has the world's second-oldest population after Japan, according to the World Bank, and elderly people appear to be more vulnerable to becoming severely ill from the virus
The country has already shed 4% of GDP in back-to-back recessions in the first two decades of the century, and recovery has been stalled for the last two years
Some tourists are being asked by hotels to undergo medical checks before checking in despite showing no symptoms of infection
Italy is the epicentre of Europe's coronavirus outbreak. More than 3,000 have been infected and at least 107 have died, the most of any country outside China, where the illness began.
According to the advisory, the government has also suspended visa on arrival (VoA) issued on or before March 3 to Japanese and South Korean nationals who have not yet entered India.
Other measures being finalised by top ministers and reported by Italian media include what promises to be an unpopular plan to play all football matches without fans
The government said that 37 people across the country have been hospitalised after they displayed symptoms of coronavirus
Passengers from 10 countries -- China, Hong Kong, Japan, South Korea, Thailand, Singapore, Nepal, Indonesia, Vietnam and Malaysia -- are already being screened at Indian airports
The curbs come as coronavirus infections have soared across northern Italy over the past few days, causing seven deaths and nearly 300 cases