Two men are assisting in police investigations into videos taken of Prime Minister Lee Hsien Loong's son, Mr Li Yipeng, in a car, as well as a fake Facebook post about the incident.

The police said in a statement yesterday that a police report has been made regarding videos taken of Mr Li, who was offered a ride in a private car.

The car was driven by a 31-year-old Singaporean man, said the police. It is understood that the vehicle was not a private-hire car.

In the videos, the man was heard asking Mr Li repeatedly to confirm his identity, his home address and also his security arrangements.

"The videos were taken without Mr Li's knowledge or permission. The police are looking into the matter with the assistance of the driver because the nature of the questions raises serious security concerns, given Mr Li's background," said the police.

Mr Li, 36, who has Asperger's syndrome, is the second of PM Lee's four children. The Prime Minister also has a daughter and two other sons.

The police added that the driver was previously convicted of taking a vehicle without the owner's consent under the Road Traffic Act.

An offence of driving without valid insurance under the Act was taken into consideration during sentencing in 2014.

Separately, it is understood that the man was involved previously in a theft-in-dwelling case and was given a warning by the police.

There was also a police report lodged against him for criminal intimidation.

The police are also investigating the circulation of a photo showing a Facebook post purportedly made by PM Lee about the incident.

The photo's content has been established to be fake, police said.

A 39-year-old man is assisting the police in their investigations into this incident. The image has been circulating online on platforms such as Telegram and Facebook.

PM Lee's press secretary, Ms Chang Li Lin, said yesterday that the Prime Minister is aware of the incident, the videos and the fake Facebook post.

She said: "It is of concern that a vulnerable person can be taken advantage of like this.

"Yipeng happens to be the PM's son, but many other vulnerable persons go about Singapore on their own, and they must be able to do so safely, without being taken advantage of or harassed and without their privacy being breached."

Ms Chang added that as the matter was being investigated by the police, PM Lee would not comment further.

PM Lee thanked members of the public who had expressed concern about the matter.