Pitched fighting intensified Monday in Yemen's second-largest city, Aden, leaving streets littered with dead bodies, as Shia rebels and their allies waged their strongest push yet to seize control of the main bastion of supporters of their rival, the country's embattled President.

The fierce fighting in the southern port city on the Arabian Sea raises doubts over the possibility of landing ground forces from a Saudi-led coalition backing President Abed Rabbo Mansour Hadi to try to carve out an enclave to which Hadi, who fled the country two weeks ago, could return.

Saudi Arabia has asked Pakistan to contribute soldiers to the military campaign, as well as air and naval assets, Pakistan's defence minister said Monday. Pakistan's parliament is debating the request and is expected to vote in coming days.

Saudi Arabia has been leading an air campaign since March 26 against the Houthis and their allies, military units loyal to Hadi's predecessor, ousted autocrat Ali Abdullah Saleh. The International Committee for the Red Cross said Monday it was still unable to get medical supplies into the capital, Sanaa, or to Aden amid the air and sea blockade by the coalition.

On Monday, Houthi fighters and pro-Saleh forces attacked Aden's Moalla neighbourhood, one of the last districts held by Hadi loyalists where the presidential palace, port facilities, TV, government offices and a military camp are located. The districts are on a peninsula that juts into the sea, meaning Hadi's forces are bottled up in the neighbourhoods.

"We are jumping over dead bodies," Radwan Allawi, a pro-Hadi fighter, told The Associated Press from Aden. He said mosque loudspeakers were calling on Hadi's supporters to defend Moalla.

"It's intense street fighting, direct fire. The only difference between life and death may be an electricity pole behind which one can hide," the 20-year-old said.

Pro-Hadi fighters destroyed three tanks deployed in Moalla by their opponents overnight, only to find new ones Monday. At least one residential building was in flames from the fighting. Coalition forces started an airdrop of weapons to Hadi's forces on Friday, but some military officials say the weapons are falling into the wrong hands.

The number of casualties was not immediately known, with medical facilities in the city overwhelmed and volunteers coming under fire from rival groups.

Mohammed Abdo Hariri, a 50-year old resident of Aden, said he fled the city during a lull in the fighting and found its streets littered with corpses and burned-out armoured vehicles. "This is a tragedy," he said.

Military experts say the intense fighting makes any ground operation in Aden far more difficult, particularly if the administrative centre falls. Saudi officials have never said publicly that the coalition intends a ground operation, but some officials in Hadi's government have called for one. Egyptian officials have previously told the AP of plans to land forces at Aden and move other troops across the Saudi border into northern Yemen once airstrikes have sufficiently weakened the Houthis and their allies.

If Aden falls, ground forces "would be deprived of that location, which can be a command centre," said retired Yemeni army general Khairi Hassan. He said coalition troops might still attempt to land at a smaller coastal town west of Aden, but at greater risk because there are few supportive forces on the ground in the area.

Mustafa al-Ani, a security analyst with close contacts in the Saudi government, said a large-scale ground operation is "out of the question," though a small number of special forces could be sent to guide airstrikes and gather intelligence. "You don't have the solid ground, the safe haven, where you can land your troops," he said of Aden.

Asked about the Pakistani comments, the Saudi ambassador to the United States played down the suggestion of an imminent ground invasion in Yemen by the coalition.

"No options are taken off the table, but I don't think we're there yet," Adel al-Jubeir told journalists in Washington. "We're in the air phase," he said.

Instead, the aim of the air campaign is "to break the back" of the Houthis and force them into negotiations, while encouraging Sunni tribes to revolt against them, said al-Ani, a Dubai-based analyst for the Gulf Research Center.

The Saudi-led airstrikes have targeted military camps, air bases, weapons depots and rebel headquarters in all but four of Yemen's 21 provinces, and civilian areas have often been hit. The United Nations estimates more than 500 people have been killed – many of them civilians – and thousands displaced by the fighting and the airstrikes.

On their 12th day Monday, the strikes began before sunset, hitting western parts of Sanaa, the Houthi's northern stronghold of Saada and in southern al-Dhale province, a supply route for Houthis fighting in Aden.

Meanwhile, the Houthis and their allies were launching a new advance into the province of Shabwa, one of the centres of Yemen's oil industry. The Houthis were seeking deals with local tribes to allow their forces safe passage to the provincial capital, Ataq, tribal leaders said. They spoke on condition of anonymity for fear of repercussions from Houthis.

Humanitarian groups have called for a pause in the fighting to allow aid to reach Yemen amid dwindling medical supplies and overstretched personnel. At least three Red Crescent volunteers were killed over the past week while evacuating wounded and retrieving the dead in Aden and al-Dhale.

The International Committee for the Red Cross said an aid plane it attempted to send to Sanaa was in Djibouti, across the Red Sea from Yemen, unable to fly because it belongs to Yemen's national carrier, Yemenia, which has halted all flights. Talks were under way with the Saudi coalition and other warring factions to arrange another cargo flight into the capital, said Marie Claire Feghali, an ICRC spokeswoman in Sanaa.

Also urgently needed, she said, is clearance to allow a surgical team to arrive in Aden from Djibouti by boat. No clearance has been granted, she said, without elaborating.

"The hospitals are exhausted," she said. "There are dead bodies on the streets in Aden. This is why we called for a 24-hour humanitarian pause in the fighting so that people can go and collect the dead."

Sarah El Deeb reported from Cairo. Asif Shahzad in Islamabad and Bradley Klapper in Washington contributed to this report.