The Cyber Security Agency of Singapore, to be established on April 1, "will provide dedicated and centralised oversight of national cyber security functions," Lee's office said in a statement.
The creation of the new agency follows a string of attacks on Singapore government portals, including the websites of the office of the prime minister and the president in 2013, as well as other hacking incidents around the world.
In neighbouring Malaysia, the website of Malaysia Airlines was commandeered yesterday by hackers who referenced Islamic State jihadists and claimed to be from the "Lizard Squad", a group known for previous denial-of-service attacks.
The agency, which will work closely with the private sector, will be involved in "strategy and policy development, cyber security operations, industry development and outreach," according to the statement.
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Minister for Communications and Information Yaacob Ibrahim will be put in charge of cyber security, it said.
Last year Yaacob said the city-state was upgrading its Cyber-Watch Centre, allowing it to track malicious activities and respond swiftly when there are security breaches.