The armed Houthi movement attacked a Saudi warship off the western coast of Yemen on Monday, causing an explosion that killed two crew members and injured three others, Saudi state news agency SPA reported.
Separately, the Houthis said they launched a ballistic missile at a Saudi-led coalition military base on the Red Sea island of Zuqar between Yemen and Eritrea on Tuesday morning, according to the group's official news channel al-Masira.
There was no immediate coalition reaction to that claim and it was unclear if there were any casualties.
The attacks signal an escalation to weeks of combat on Yemen's western coast between the Iran-allied Houthis and the coalition backing Yemen's internationally recognized government.
"A Saudi frigate on patrol west of Hodeidah port came under attack from three suicide boats belonging to the Houthi militias," the Saudi-led coalition fighting in Yemen said in a statement on SPA.
One of the boats collided with the rear of the vessel, causing an explosion and a fire that killed two crew members and wounded three others.
The Houthi movement's al-Masira channel contradicted this account and quoted a military source saying the explosion was caused by a guided missile.
It was at least the second attack by the Houthis on ships off the coast of Yemen in the last six months.
The group is engaged in battles on the mainland with coalition troops and pro-government fighters, who are trying to advance northward to deprive the Houthis of Red Sea ports.
The Saudi-led coalition warned the attack on the ship "would impact international navigation and the flow of humanitarian assistance to the port for Yemeni citizens."
Saudi Arabia and its Gulf Arab allies have carried out thousands of bombing raids in Yemen since March 2015 in a campaign to try to restore the ousted administration government of President Abd-Rabbu Mansour Hadi.