The Houthis have stepped up the missile and drone attacks they began last month against international vessels sailing through the Red Sea, in response to Israel's assault on the Gaza Strip.
The attacks this week forced oil major BP and a slew of freight firms including Maersk to divert shipments normally made through the Suez Canal around the Cape of Good Hope, adding days to journey times and incurring higher costs.
Austin, who is on a trip to Bahrain, home to the US Navy's headquarters in the Middle East, said the United Kingdom, Bahrain, Canada, France, Italy, Netherlands, Norway, Seychelles and Spain were among nations involved in the Red Sea security operation.
The group will conduct joint patrols in the southern Red Sea and the Gulf of Aden.