The training exercise yesterday came ahead of a port call in the Philippines, which along with several other nations is embroiled in disputes with Beijing over its claim to the strategic waters.
The demonstration, during a visit by Philippine generals and journalists, was held just days after Beijing flexed its own military muscle with a huge naval drill involving its sole aircraft carrier and dozens of other vessels several hundred kilometres to the north.
Koehler acknowledged "there's a lot of disputes" over the area but insisted the carrier group was transiting through international waters.
The US, a long-time ally of the Philippines, is not party to any of the disputes but says it wants to keep the crucial waterway open to shipping.
"If all the navies are operating in accordance with the international norms and law, which is what we're doing and what we've seen all the navies that are operating in and around the South China Sea (do), that's the whole point," Koehler said.
Its neighbours, particularly some of those involved in maritime disputes over the waters, have expressed fears China could eventually restrict freedom of navigation and overflight.
Koehler said his strike group's presence in the area was planned well in advance and it was "probably by happenstance" that its mission coincided with the Chinese drill.
"Certainly in the last few years China has increased their naval capacity. We certainly see that," he said.
The Roosevelt's captain, Carlos Sardiello, said it was "in the vicinity" of Reed Bank, a supposedly gas-rich undersea formation claimed by Manila and Beijing, and about 270 nautical miles from Manila.
Beijing has previously protested over similar US Navy manoeuvres in the South China Sea.
US warships regularly conduct "freedom of navigation" operations near islands controlled by Beijing.
The carrier group was en route to Manila, having returned to the Pacific after its warplanes launched more than 1,000 sorties last year, both against the Islamic State group in Iraq and Syria and also in Afghanistan.
Compared with the 11 active carriers in the US Navy, China currently has just one.
But it has made no secret of its desire to build up its naval forces and last month announced an 8.1 percent increase in military spending to 1.11 trillion yuan (USD 175 billion).