South Korean pop icon Rain has come under fire after reports revealing his relationship with a top TV actress suggested he might be flouting the terms of his compulsory military service.

Rain's relationship with Kim Tae-Hee, a major TV drama star with a massive following in Japan, was first reported Tuesday by a tabloid magazine, sparking a fan frenzy on entertainment websites and social networks.

The magazine published photos showing Kim, 32, wearing a cap and surgical mask, getting into a car driven by the singer, who is halfway through the two-year military service that is mandatory for Korean men.

"They are currently getting to know each other with feelings for each other," Kim's agency said in a statement later Tuesday, confirming the two had been dating for about a month.

Fan excitement over the match-up between two of the country's most high-profile celebrities was tempered by questions over how -- as reported by the magazine -- the couple had managed numerous dates over the past four weeks.

During their military service, Korean men are largely confined to their barracks and given little free time.

"I don't care whoever Rain dates ... but what kind of soldier gets Christmas holiday, where most guys toil shovelling piles of snow at the frontline units in bitter cold?" said one online commentator.

One of the tabloid pictures of the couple showed Rain, 30, driving a private car in military uniform, contrary to service guidelines, and not wearing his army beret.

The defence ministry's website has been bombarded with messages calling for Rain to be disciplined, with more than 3,000 people signing an online petition urging an investigation.

"Rain has to serve twice, just like Psy did!" said another online comment, referring to the "Gangnam Style" singer who was forced to repeat his military service after it emerged he had furthered his showbiz interests during his first stint.

Rain has been serving as an "entertainment soldier" who appears in military-run TV and radio programmes aimed at boosting morale.

The singer, whose real name is Jung Ji-Hoon, is one of the biggest names in the world of K-pop which commands a huge following in South Korea and across much of Asia and beyond.

A defence ministry spokesman insisted Rain had earned holiday in line with military rules, but added that his army unit was "looking into the matter" given the public clamour.

"We advise soldiers to wear proper military outfit including a beret during a holiday but a failure to do so is not a punishable crime," the spokesman told AFP.