Malaysia has filed an application at the International Court of Justice (ICJ) to declare that the waters surrounding Pedra Branca are within its territorial waters.
In response, Singapore says the move is puzzling, without merit, and one it will oppose.
The bid, filed on Friday, calls on the court to clarify its 2008 judgment which awarded Pedra Branca to Singapore, and neighbouring Middle Rocks to Malaysia.
The ICJ also found nearby South Ledge belongs to the country in whose territorial waters it is sited.
News of the latest Malaysian bid broke yesterday which, ironically, was the day Singapore was marking 50 years of national service, set up to boost the Republic's security.
In its application, Malaysia also asked the court to declare that South Ledge is in Malaysia's territorial waters and therefore belongs to it, the ICJ said in a press statement.
Singapore's Ministry of Foreign Affairs (MFA) said yesterday: "In our view, the ICJ judgment is clear and unambiguous. Malaysia's request for the ICJ to interpret the judgment is puzzling. Singapore will therefore oppose Malaysia's application for interpretation, which we consider to be both unnecessary and without merit."
Malaysia's fresh challenge comes months after it filed a separate bid to revise the 2008 ruling in February, citing newly discovered facts.
Both countries had taken the dispute over Pedra Branca, Middle Rocks and South Ledge to the ICJ in The Hague.
All three features in the Singapore Strait are about 40km east of Singapore's main island.
The court delivered its ruling in 2008. MFA said the ICJ "also noted it had not been mandated to draw the line of delimitation with respect to the territorial waters of Malaysia and Singapore in the area".
The two countries set up a Malaysia-Singapore Joint Technical Committee (MSJTC) to implement the ruling, and it was tasked with delimiting maritime boundaries between the territorial waters of both.
But according to Malaysia, the MSJTC reached an impasse in November 2013.
Malaysia claims that both sides have been unable to agree on what two points of the ruling mean: that sovereignty over Pedra Branca belongs to Singapore, and that sovereignty over South Ledge belongs to the state in whose territorial waters it is located.
Malaysia argues this "ongoing uncertainty" as to who is sovereign over the disputed areas "continues to complicate the task of ensuring orderly and peaceful relations", the ICJ said. Malaysia says "the need to achieve a viable solution to the dispute is pressing", considering the "high volume of aerial and maritime traffic in the area", the ICJ added.
But MFA said the ICJ judgment was final and without appeal. "Singapore and Malaysia had agreed to honour and abide by the judgment and had established the MSJTC," it said.
Malaysia's fresh application "is additional to, and separate from" its February bid to revise the 2008 judgment, MFA said. Singapore filed its written observations in response to that with the ICJ in May.
A revision application seeks to revise or alter a judgment based on purported newly discovered facts, while an interpretation application seeks to clarify a judgment.
Dr Mustafa Izzuddin of the ISEAS - Yusof Ishak Institute sees Malaysia's bid as a "calculated strategic attempt" to show to voters ahead of upcoming elections that the government is defending the national interest. He adds that it "is unlikely to stand up to scrutiny".
MFA said Singapore will file its written observations on the interpretation application in due course.
"Just as we are confident of our case on the revision application, we are also confident that we are on strong grounds to oppose this latest application by Malaysia for interpretation. Singapore is committed to resolving these issues in accordance with international law," it added.