SINGAPORE - Singapore's leaders, reflecting on the Sydney hostage-taking incident and the loss of lives, said it showed that the threat from terrorism remained a cause for concern and that Singaporeans need to be alert - and stay united should any such incident occur here.

Prime Minister Lee Hsien Loong, Deputy Prime Minister Teo Chee Hean, Defence Minster Ng Eng Hen and Senior Minister of State (Home Affairs and Foreign Affairs) Masagos Zulkifli all commented in Facebook posts on Tuesday on the 16-hour siege in which a gunman took hostages in a Sydney cafe on Monday.

The incident ended in the early hours of Tuesday morning when heavily-armed security forces stormed the Lindt Chocolate Cafe in the city centre. The gunman and two other people died in the incident and at least four others were injured.

PM Lee, who expressed sadness at the loss of innocent lives, recalled that he had a briefing and dialogue with community and religious leaders on extremist terrorism last month.

"We talked about how it remained a live threat to us, and in particular the danger of self-radicalisation. This incident teaches us to keep up our guard," he said in his post.

"Despite all our precautions, we can never completely rule out such an incident here. If it ever happens, we need the cohesion and resilience to deal with it calmly and as one united people, and not let it divide or destroy our society."

At the dialogue with community and religious leaders on Nov 29, PM Lee spoke about how the ongoing conflict in Syria and Iraq had seen terrorist elements in South-east Asia regroup and become more active, and said the Government had to do what was necessary to protect Singapore.

This included getting the support of the community, being vigilant domestically and "taking swift action to neutralise threats to Singapore, or people who may get themselves in trouble", he said at the time.

He had also made the point that while eradicating terrorism will be a difficult and long-term fight, Singapore will prevail "provided we work together and be open with each other and share and come closer together".

DPM Teo, who is Coordinating Minister for National Security and Home Affairs Minister, said in his post that Singapore has been "in touch with our Australian and other counterparts to find out more details about the incident".

"The incident shows that terrorist attacks by individuals can take place even when there is heightened security. Everyone in Singapore can play a part to help pre-empt and prevent such attacks by remaining vigilant and reporting any suspicious activities to the authorities promptly," he said.

A key aspect that leaders here have underlined is the need for Singaporeans to remain united.

As DPM Teo put it in his post: "Just as importantly, if such an attack should take place, we should all face it together in a calm and resolute way, and cooperate with the authorities to resolve it appropriately. Any such terrorist activities are a danger to all communities in Singapore, and all Singaporeans should remain united and continue to work together to overcome them."

Expressing a similar sentiment, Dr Ng, who also attended the Nov 29 dialogue involving PM Lee and DPM Teo, said in his post: "We must not allow any person or group to weaken or fracture the strong ties that we have painstakingly built to forge a harmonious multi-racial and multi-religious nation in Singapore."

The Sydney incident showed "how even one person can inflict much harm to society", Dr Ng said, adding that at the meeting with religious and community leaders, he also said that despite efforts of security and other agencies, no one could guarantee that Singaporeans would not be affected by threats posed by extremist terrorism.

But he was "reassured that leaders of different faiths and backgrounds understood that if any incident should ever happen, we must come together, to support and protect each other.

"We must not allow any person or group to weaken or fracture the strong ties that we have painstakingly built to forge a harmonious multi-racial and multi-religious nation in Singapore," Dr Ng said in his post.

Mr Masagos, in his message on Facebook, noted that one of the victims, Sydney barrister Katrina Dawson, was a young mother of three children, and that the other, cafe manager Tori Johnson, was well liked and was just doing his job.

"It's sad that madness brings demise to young innocents - I can understand their children and loved ones growing up angry with Muslims. But I hope they will heal because only forgiveness will stop this madness from reaping its malicious intent," he said.