The fact Houthi media has highlighted the current meetings with the Iranians shows this is not clandestine, but rather an open call.
India's navy deployed three destroyers to maintain a deterrent presence in various locations after an attack near India's waters.
Vessels in the area were advised to transit with caution and report any suspicious activity.
The land route is cheaper and faster than sea transport at the moment.
Iran warned that any attempt by the US to establish an international naval coalition "will be faced with extraordinary problems."
A cargo ship was hit by an unknown object, sparking a fire, off the coast of Yemen.
Ambrey said the ship had reported a group claiming to be the "Yemeni Navy" had demanded the change in course.
The Houthi statements and widespread coverage of this issue in their media show they are using Gaza as a new rallying cry; they want to potentially distract from problems at home, and show strength.
American and French navies have strengthened their presence in the Red Sea to protect vessels from the risk of seizure or attack by the Houthis.
There was no damage to US Navy vessels or injuries to US personnel in the attack, said the US official, who declined to be named.