South Korea reported its first two deaths from an outbreak of Middle East Respiratory Syndrome (MERS) that has infected 25 people in two weeks, as public alarm grew and officials scrambled to contain the outbreak.

South Korea has isolated more than 700 people for possible MERS infection, which is caused by a coronavirus from the same family as the one that triggered the deadly 2003 outbreak of Severe Acute Respiratory Syndrome (SARS). 

MERS has a much higher death rate than SARS and there is no cure or vaccine.

The World Health Organization (WHO) puts the total number of cases globally at 1,161, with at least 436 related deaths. It said no mutation had been detected in the virus in South Korea, and it did not appear to be spreading easily.

A 57-year-old woman, who had contact with South Korea's first patient, died of acute respiratory failure on Monday, the Health Ministry said. 

She died at a hospital in Gyeonggi, the country's most populous province which surrounds the capital Seoul.

A 71-year-old man who had been on respiratory support with a history of kidney ailments also died. Officials did not disclose his location.

South Korea's health ministry reported seven new cases on Tuesday, including the woman who died, bringing the total number of cases to 25. 

South Korea now has the third highest number of cases after Saudi Arabia and the United Arab Emirates

Officials have come under criticism from many in South Korea for not naming the hospitals where people have been treated, which has fueled widespread speculation.

China last week reported its first MERS case, that of a South Korean man who tested positive after breaking a voluntary house quarantine and traveling to Hong Kong and on to mainland China.

South Korean Deputy Prime Minister Choi Kyung-hwan said the government's credibility was at stake after criticism against authorities for failing to contain the virus after the first patient's symptoms were initially overlooked.

The death rate from MERS, first identified in humans in 2012, has been 38 percent, according to WHO figures, with older patients and those with existing respiratory and renal ailments at greater risk, according to a South Korean doctor. 

However, experts said that figure may overstate the fatality rate as patients with little or no symptoms might go undetected.

By comparison, the death rate from SARS was 9 to 12 percent, rising above 50 percent for patients over 65, according to the U.S. National Library of Medicine.

The WHO has so far not recommended trade or travel restrictions for South Korea.

But South Korean border control authorities have put a ban on overseas travel for people isolated for possible infection, a health ministry official said.

South Korea's Hyundai Motor said it had asked employees to avoid traveling to the Middle East, while Samsung Electronics said it was screening employees twice a day in South Korea for fever, and would refrain from large-scale events.

58 schools and kindergartens in Gyeonggiprovince, home to the hospital where the first death occurred, were shut for the week

Some tour agencies have started seeing overseas groups cancelling trips to South Korea, with about 2,500 cancellations by Monday