Iran issued its most dire warning yet on Tuesday about the outbreak of the new coronavirus ravaging the country, suggesting millions could die in the Islamic Republic if the public keeps travelling and ignoring health guidance.

A state television journalist who also is a medical doctor gave the warning only hours after hard-line Shia faithful had last night pushed their way into the courtyards of two major shrines that had just been closed over fears of the virus. Meanwhile, Iran's supreme leader issued a religious ruling prohibiting unnecessary travel in the country.

Roughly nine out of 10 of the over 18,000 cases of the new virus confirmed across the Middle East come from Iran, where authorities denied for days the risk the outbreak posed. Officials have now implemented new checks for people trying to leave major cities ahead of Nauroz, the Persian New Year, on Friday, but have hesitated to quarantine the areas.

That's even as the death toll in Iran saw another 13 per cent increase on Tuesday. Health Ministry spokesman Kianoush Jahanpour said the virus had killed 135 more people to raise the total to 988 amid over 16,000 cases.

Jordan meanwhile prepared for a shutdown of its own over the virus, banning gatherings drawing more than 10 people, as neighbouring Israel issued its own strict new guidelines for life under the coronavirus threat.

Most people infected by the new coronavirus experience only mild or moderate symptoms, such as fever and cough, and recover within weeks. But the virus is highly contagious and can be spread by people with no visible symptoms. For some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia.

The Iranian state TV journalist, Dr Afruz Eslami, cited a study by Tehran's prestigious Sharif University of Technology, which offered three scenarios. If people begin to cooperate now, Iran will see 120,000 infections and 12,000 deaths before the outbreak is over, she said. If they offer medium cooperation, there will be 300,000 cases and 110,000 deaths, she said.

But if people fail to follow any guidance, it could collapse Iran's already-strained medical system, Eslami said. If the medical facilities are not sufficient, there will be four million cases, and 3.5 million people will die, she said.

Eslami did not elaborate on what metrics the study used, but even reporting it on Iran's tightly controlled state television represented a major change for a country whose officials had for days denied the severity of the crisis.

Underlining that urgency was the fatwa issued by Supreme Leader Ayatollah Ali Khamenei, which prohibited unnecessary travel. It comes as the public ignored repeated warnings and pleas from security forces. Such a decree is a rare move by Khamenei, who has the final say on all state matters.

Late on Monday night, angry crowds stormed into the courtyards of Mashhad's Imam Raza shrine and Qom's Fatima Masumeh shrine. Crowds typically pray there 24 hours a day, seven days a week, touching and kissing the shrine. That's worried health officials, who for weeks ordered Iran's Shia clergy to close them.

Earlier on Monday, the state TV had announced the shrines' closure, sparking the demonstrations.

"We are here to say that Tehran is damn wrong to do that!" one Shia cleric shouted at the shrine in Mashhad, according to an online video. Others joined him in chanting: "The health minister is damn wrong to do that, the president is damn wrong to do that!"

Police later dispersed the crowds, state media reported. Religious authorities and a prominent Qom seminary called the demonstration an insult to the shrine in a statement, urging the faithful to rely on wisdom and patience amid the closure.

Iran's shrines draw Shias from all over the Mideast for pilgrimages, likely contributing to the spread of the virus across the region. Saudi Arabia earlier closed off Islam's holiest sites over the fear of the virus spreading.

Iranian President Hassan Rouhani on Tuesday said: "Despite the closures, our soul is closer to the saints more than at any time."

State TV reported that Iran had deployed teams to screen travellers leaving major cities in 13 provinces, including the capital, Tehran. But Iran has 31 provinces and authorities haven't taken the step to lock down the country like in the allied nations of Iraq and Lebanon.

The teams check travellers' temperatures and will send those with fevers to quarantine centres. Iran has been urging people to stay home, but many have ignored the call.

Apparently, in efforts to curb the spread of the virus, Iran has released 85,000 prisoners on temporary leave, judiciary spokesman Gholamhossein Esmaili said on Tuesday. He said that included half of all security-related prisoners, without elaborating. Western nations have called on Iran to release dual nationals and others held allegedly as bargaining chips in negotiations.

Among those released is Mohammad Hossein Karroubi, the son of opposition leader Mehdi Karroubi, who was in jail for nearly two months.

Egypt, which has 166 confirmed cases of the new virus including four fatalities, announced on Tuesday the lockdown of the Red Sea province that includes the popular resort town of Hurghada. Local authorities barred workers in all tourist sites, hotels, bazaars and restaurants from leaving the province and imposed a 14-day quarantine, according to a document from the Red Sea governor's office obtained by The Associated Press.

They also banned all visitors to the province for the next two weeks.

The kingdom of Jordan deployed troops outside of major cities to block travel on Tuesday. It also ordered newspapers to cease publishing, banned gatherings of more than 10 people and established a quarantine zone at Dead Sea hotels. It halted all private sector work and public transportation as well.

In Oman, the sultanate announced anyone coming from abroad would be subject to quarantine.

Meanwhile, in Israel, the Defence Ministry plans to use near-empty hotel facilities, ravaged by the crash in tourism, as recovery centres for patients diagnosed with COVID-19, the illness caused by the virus. Israel also called on citizens to remain in their homes, closing parks, museums, libraries, beaches and other public areas.

Only short walks outside with family members and pets are permitted.