Singapore's Ministry of Defense, Ng Eng Hen, said the bilateral relationship between the United States and China is the most important one for the Asia-Pacific region.
Royal Navy frigates HMS Sutherland and HMS Argyll and amphibious assault HMS Albion are being deployed to "send a clear message" to China and North Korea, Williamson said.
However, a Chinese military official dismissed the comments as "irresponsible".
"China's policy in the South China Sea stands in stark contrast to the openness that our strategy promotes, it calls into question China's broader goals", Mattis said.
French Defence Minister Florence Parly called on countries to abide by worldwide law in the South China Sea, saying that France would persistently object to the creation of any claim to de facto sovereignty of the islands there.
U.S. Secretary of Defence Jim Mattis speaks at the IISS Shangri-la Dialogue in Singapore June 2, 2018.
At the forum, Beijing's representatives responded to the French and British plans by saying the South China Sea is free and open for all to travel through, and there would be no restrictions on normal freedom of navigation.
He also said the United States would continue to support Taiwan, the self-governing island that China claims as its territory, with military and other assistance.
China has also landed heavy bombers on Woody Island in the Paracel Islands.
Weeks earlier, USA intelligence announced there was a high possibility Beijing had deployed anti-ship and anti-aircraft missiles as part of ongoing military exercises.More news: Optimism as tobacco smokers reduce by 29 million globally
Earlier in the week, Mattis warned the United States will continue "a steady drumbeat" of naval exercises to challenge China's territorial claims in the waterway, and this weekend said, "there are consequences that will continue to come home to roost" if China does not act more transparently and cooperatively in the region.
"Despite China's claims to the contrary, the placement of these weapons systems is tied directly to military use for the purposes of intimidation and coercion", Mattis said at the annual Shangri-La Dialogue.
Six countries have competing claims in the sea, but China has backed its own with island-building and patrols.
The U.S. Navy on Sunday conducted the latest of its "freedom of navigation" patrols near China-occupied features to demonstrate the right to sail through what it considers to be worldwide waters.
"We do not do freedom of navigation for America alone, we do freedom of navigation for all nations. we do not see it as a militarization by going through what has traditionally been worldwide water space".
"We believe nations should follow agreed rules but this is being ignored by some and what this does is it undermines peace and prosperity of all nations", he said. "If China's islands and reefs are continuously threatened by activities under the name of so-called freedom of navigation, China will eventually station troops on these reefs".
He also said the U.S. recognised that China had a role to play in the region.
Wang Mingliang, a defence expert cited in the statement, said the exercises on islands in the were aimed at helping the air force "strengthen its combat capability to deal with maritime security threats".
Much of the speech was focused on longer-term challenges in the region known as the Indo-Pacific, a phrase used throughout India and Southeast Asia and recently embraced by the Trump administration.
Nevertheless, he did point out that the UK, France and Australia had also been asserting their rights of passage in the region.