Police are investigating 17 people, including civil society activists, over whether they committed the offence of participating in an illegal assembly.
The group includes sociopolitical website editor Terry Xu and blogger Kirsten Han, said the police in a statement yesterday.
The group had held a vigil on July 13 outside Changi Prison Complex for 29-year-old Malaysian Prabagaran Srivijayan, who was convicted of importing 22.24g of heroin into Singapore. He was hanged at dawn on July 14.
In a Facebook post, Ms Han said police officers at the scene confiscated tea lights and photos of Prabagaran, and the group complied with their orders. "We were then told that it would be all right for us to stay, as long as we did not light any more candles. We did not light any more candles," she wrote last Wednesday.
Mr Xu, the chief editor of The Online Citizen, said he was stopped at immigration last Wednesday and prevented from leaving the country.
He and Ms Han said they had not been informed earlier that they could not leave the country until after being questioned by the police.
The move was criticised by Human Rights Watch in a statement last Thursday.
"Both the belated criminal investigation and the travel ban have all the hallmarks of a harassment campaign against those who dare to peacefully criticise the Government," said its deputy Asia director Phil Robertson.
In response to media queries on travel restriction and typical procedures for such cases, the police said: "Organising or participating in a public assembly without a police permit is illegal in Singapore. There are rules on where public assemblies can take place, to promote, advocate causes."