The US is stepping up its rhetoric on Iran as it warns it is considering “all appropriate responses” after Houthi rebels attacked three merchant ships in the Red Sea on Sunday, as the Iran-backed fighters continue to harass US and international interests in the region.

After the attacks, a US warship operating nearby responded to distress calls from merchant ships, shooting down three aerial drones during the day, US Central Command said in a statement.

Although Defense Department officials said they did not believe the militants were targeting the US warship – the Arleigh Burke-class destroyer USS Carney – the series of attacks on merchant ships “poses an immediate threat to international trade and maritime security”, said the Central Command.

Although the attacks were carried out by the Houthis, the US has “every reason to believe” that they were “fully supported by Iran”, according to the statement. “The United States will consider all appropriate responses in full coordination with its international allies and partners.”

The language is an explicit threat to Iran that the US may respond to the attacks, the latest in the region in a series of others. Iran-backed militants have also attacked US troops in Iraq and Syria at least 74 times since October 17.