Thousands of people marched through Yemen's capital Sanaa on Friday to mark the sixth anniversary of a Saudi-led military intervention against Huthi rebels, as the United Nations renewed calls for a ceasefire.

The Iran-backed Huthis overran Sanaa in September 2014 and went on to capture most of the country before a coalition led by Saudi Arabia intervened in March 2015 to bolster the government.

Since then, tens of thousands of people have been killed and millions displaced, according to international organisations, in what the UN calls the world's worst humanitarian crisis.

On Monday, Saudi Arabia offered the Huthis a "comprehensive" UN-supervised ceasefire to try and end the brutal conflict, but the rebels have dismissed the initiative as "nothing new".

"If they want peace, they must stop their aggression and end the blockade imposed on the Yemeni people," senior Huthi official Deif Allah al-Shami told AFP on the sidelines of Friday's rally.

"We don't need any initiative," he said, referring to the Saudi peace offer.

Around him, Huthi supporters held up pictures of rebel leader Abdul Malik al-Huthi, Yemeni flags and signs that read "death to America, death to Israel, curse upon the Jews, victory to Islam".

Huthi security forces, masked and in military garb, were deployed in Sanaa for the rally, where many protesters brandished weapons or raised clenched fists as they shouted slogans against Saudi Arabia.

- Ceasefire efforts -

Hours earlier, a projectile attack sparked a fire at an oil terminal in the southern Jizan province of Saudi Arabia, the country's energy minister announced, without saying who was behind the attack.

And on Thursday the Saudi-led coalition said it intercepted several explosives-laden drones fired towards the kingdom by the Huthis.

The rebels, who have recently escalated attacks on the oil-rich neighbouring kingdom, including on its energy facilities, claimed responsibility for the Jizan attack in a video.

Saudi Arabia's ceasefire offer was the second since last year.

The kingdom also proposed to re-open the international airport in Sanaa and restart political negotiations between the warring sides.

UN special envoy Martin Griffiths on Friday met Huthi official Mohammed Abdelsalam in neighbouring Oman to discuss ways of restoring peace in Yemen.

"They discussed the urgency to agree on opening Sanaa airport and... entering a nationwide ceasefire and resuming the political dialogue under a UN framework to pave the way for sustainable peace," Griffiths' office said in a tweet.

Talks also centred on "easing restrictions on Hodeida", the Red Sea port that is a lifeline gateway for food, fuel and humanitarian aid entering Yemen.

The Huthis have been demanding the lifting of a Saudi-led air and sea blockade that the coalition says it imposed to prevent the smuggling of weapons to the rebels from Iran -- allegations Tehran denies.

The Saudi ceasefire offer and UN efforts to find a solution come as the US administration of President Joe Biden is also pushing to try to end the conflict.

Washington's special envoy for Yemen, Tim Lenderking, visited the region last month and made contact with the Huthis in Oman as well, sources told AFP. He is set to return to press for a ceasefire.

On Friday, the US condemned the latest attack on Saudi oil infrastructure, saying the strikes "are a clear provocation meant to perpetuate the conflict".

"The Huthis' actions are... jeopardizing peace efforts at a critical moment when the international community is increasingly united behind a ceasefire and a resolution of the conflict," State Department spokesman Ned Price said in a statement.

Analysts have said that Riyadh's ceasefire offer is an attempt to portray the rebels as aggressors while the kingdom seeks an exit from the military quagmire.

- 'Yemen is desperate' -

With no quick solution in sight, the UN humanitarian agency OCHA on Friday lamented the consequences of six years of war in Yemen in a series of tweets.

"Six years of war mean six years of hunger, six years of displacement, six years of destruction, six years of misery and lives lost," it said.

"Yemen is desperate for peace and time is now for all to act," OCHA added, using the hashtag "#YemenCantWait".

Famine could become part of the country's "reality" in 2021, UN Development Programme chief Achim Steiner told AFP earlier this month after a donor conference raised $1.7 billion in aid for Yemen -- half its target.

More than 16 million Yemenis will face hunger this year, and nearly 50,000 are already starving in famine-like conditions, according to the latest UN figures.

Around two thirds of Yemen's 29 million people depend on some form of aid for survival.

"Six years of war have shown failure," the Huthi official Deif Allah al-Shami said Friday.