"It's great to be Singaporean today," read a mocking headline in a section of www.pmo.gov.sg next to the group's trademark Guy Fawkes mask, a symbol of anti-establishment defiance worldwide.
Next to it was another image saying: "PM Lee warns hackers: We will track you down even if you think you're 'anonymous'".
Another message read: "ANONYMOUS SG WAS HERE BIATCH", using a pejorative in online youth slang.
The defaced section was quickly taken offline after the hacking incident surfaced in a posting on Facebook. The rest of the site was working normally.
In a statement issued early Friday, the government's Infocomm Development Authority said it was investigating the incident.
"The PMO (Prime Minister's Office) main website is still working, and we are working to restore the page that has been compromised," it said.
Social media and independent websites have become the main arenas of political debate in Singapore, whose mainstream newspapers and broadcasters are widely perceived to be pro-government.
The hacking took place a day after Lee told local journalists that his government would "spare no effort" in going after Anonymous members who last week threatened to wage a cyber war against Singapore.
"Our IT network, the Internet, our communications have become an essential part of our business and our lives now," the Today newspaper quoted him as saying.
"And, therefore, when somebody threatens to do harm to it... we take that very seriously and we will spare no effort to try and track down the culprits and if we can find him, we will bring him to justice and he will be dealt with severely."
It was Lee's first comment since a person claiming to be from Anonymous threatened to mount cyber attacks against the government in protest at new licensing rules for news websites.
In the video posted on YouTube on October 31, a person speaking with a computer-digitised voice and wearing a Guy Fawkes mask said the group would "go to war" with the Singapore government.
A day later a person claiming to be affiliated with Anonymous hacked a reporter's blog on the website of the Straits Times newspaper.
The hacker also warned of further attacks on the tightly governed island's technological infrastructure if demands for greater Internet freedom were not met.
Singapore strictly regulates the traditional media. Its new Internet rules have sparked anger in the blogging and social media community, which says the rules are designed to muzzle free expression.
Authorities insist the new licensing rules do not impinge on Internet freedom.
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