Malaysia's Foreign Minister Rais Yatim described it as a 'win-win' judgment and said that both countries would 'forge ahead' in their bilateral relationship.
In Singapore, Prime Minister Lee Hsien Loong declared that he was pleased with the result, saying that resorting to the ICJ was 'a good way for (the two countries) to resolve disagreements or problems while maintaining good relations with each other'.
In Malaysia, Deputy Prime Minister Najib Razak called it a 'balanced decision', with Malaysia 'partly successful' in its territorial claims.
The two hours at the ICJ were suspense-filled and had the Singapore delegation, led by Professor Jayakumar, on the edge of their seats for much of the time.
For the first hour, it actually seemed as if the court would find in Malaysia's favour.
Reasoning from various historical writings, treaties and letters relevant to the case, the court decided that these showed that the Sultanate of Johor possessed original title to the island, dating back to the 16th century.
This meant that the court rejected Singapore's argument that Pedra Branca was terra nullius, that is, belonged to no one, in 1847 when the British took ownership of it and built Horsburgh Lighthouse there.
But things started looking up in the second hour, when the focus shifted to the various activities that Singapore had carried out on the island in the latter half of the 20th century.
These included its investigation into marine accidents in the waters around Pedra Branca, control of visits to the island, plans to reclaim it and installation of military communications equipment there.
The court found that all these activities were carried out a titre de souverain, that is, in a manner that conferred title on the state responsible.
It also noted Malaysia's failure to protest against these acts, all of which - except for the installation of military equipment - it had noticed.
The court also highlighted as of 'major significance' a 1953 letter from the Johor Acting State Secretary informing the colonial authorities in Singapore that Johor did not claim ownership over Pedra Branca.
The reply made clear that in 1953, Johor understood that it did not have sovereignty over Pedra Branca.
That reply would also have left the authorities in Singapore with no reason to doubt that Britain had sovereignty over the island, the court concluded.
The court thus judged that although Johor had possessed an original title to Pedra Branca, that title subsequently passed to Singapore.
The dispute between Singapore and Malaysia over sovereignty of the island arose in February 1980, when Singapore protested against a 1979 Malaysian map that placed Pedra Branca within its territorial waters.
The court ruled that by that critical date, sovereignty over the island had already passed to Singapore.
'The court concludes that sovereignty over Pedra Branca belongs to Singapore.' As Judge Al-Khasawneh pronounced these words, smiles broke out on the Singapore side of the Peace Palace's Great Hall.
The 16 judges of the ICJ voted 12 to four in Singapore's favour.
On the issue of Middle Rocks, the court said that Malaysia's claim of original title still held, as there had been no activities on Singapore's side which made it pass to Singapore.
While the ICJ ruling has settled sovereignty issues, other issues remain.
For one thing, Singapore and Malaysia have to discuss how to delimit the territorial waters in the Pedra Branca and Middle Rocks area.
There will have to be 'sensitive management' of navigational rights, said Mr S. Kesavapany, a former Singapore high commissioner to Malaysia.
'For instance, both our navies will go through the waters, so you need clear understanding of the circumstances under which this can be done,' he said.
A joint technical committee is already in place to discuss these and related issues.
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