The Houthis said they had been targeting a battleship of the coalition in response to an air strike in Yemen's Hodeidah province on Monday. The group, which controls most of northern Yemen, has launched a series of missile strikes on Saudi Arabia, including the capital Riyadh, in recent days.
In a statement carried by Saudi media, the coalition said the oil tanker was in international waters when it came under "Houthi-Iranian attack" at around 13:30 local time.
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A coalition warship conducted a "swift intervention" foiling the attack, it said, without identifying the type of weapon used in the assault.
"As a result of that attack, the tanker was subjected to a slight but ineffective hit and it resumed its naval course northwards, escorted by a coalition warship," the statement said.
A text message from the media department of the Houthi-run Yemeni military said naval forces had "targeted a battleship belonging to the coalition in response to the bombardment of displaced people in Hodeidah". It gave no further details.
The message referred to an air strike by the Saudi-led coalition on Monday in Hodeidah that destroyed a house and killed 12 civilians from the same family, including seven children.
UN piles on pressure
UN Secretary-General Antonio Guterres urged the warring sides in Yemen on Tuesday to reach a political settlement to end a conflict now in its fourth year that has left 22 million people in urgent need of aid.
His Special Envoy Martin Griffiths will head to the United Arab Emirates, Oman and the Yemeni government-held city of Aden in the drive for peace, Guterres told reporters.
Griffiths has already held talks with both sides in the war which has drawn in regional powers, meeting Houthi authorities who hold the capital Sanaa as well as internationally-recognised Yemeni president Abd-Rabbu Mansour Hadi and Saudi officials in Riyadh.
Guterres said he saw "positive perspectives" for preparing a plan of action "to lead to an effective inter-Yemeni dialogue able to achieve a political solution, with of course the involvement of all those that are relevant in this conflict".
"I am optimistic about that possibility," the United Nations chief added.
The war has killed more than 10,000 people, displaced more than 2 million and driven the country to the verge of famine.
Guterres was speaking on the sidelines of a UN pledging conference a day after an air strike by the Saudi-led coalition that supports Hadi's government killed 12 civilians in the coastal city of Hodeidah. Houthi forces later targeted Saudi Arabia's southern border area with a missile.
He announced that more than $2 billion has been pledged towards a UN humanitarian appeal of $3 billion for Yemen this year. It includes $930 million from Saudi Arabia and the UAE which lead the coalition air strikes.
"As important as the financial contributions to the conference is the commitment of parties to the conflict to come together to put an end to the war," Guterres said.
When the Houthis fired missiles at Riyadh last November, the Western-backed coalition responded by shutting Yemen's airports and ports. The UN said that blockade raised the danger of mass starvation and it was partially lifted.
Guterres told the conference: "All ports must remain open to humanitarian and commercial cargo, the medicines, food and the fuel needed to deliver them."
Most humanitarian aid enters Yemen through Hodeidah but the government accuses Houthis who control the port of smuggling weapons through it.
Yemeni Foreign Minister Abdel-Malek al-Mekhlafi called for a return to the negotiating table and said that his government was working to open ports and airports to aid.
"We need to find the ideal solution which is a return to the talks table, to put an end the war, to return to a sustainable system supported by the people of Yemen," he said, adding that this should include "the putschist parties" - referring to the Houthis - and those supported by the international community.
Jan Egeland, secretary-general of the Norwegian Refugee Council, called for a ceasefire and end to the war.
"We also ask Saudi Arabia, the United Arab Emirates, Iran - who are supporting opposing sides - and for that matter, the United Kingdom, the United States, who are earning enormous sums of money on arms sales to this conflict, to push the parties to the table," he told Reuters.