Rebels have engaged in intense street battles with forces loyal to President Abd-Rabbu Mansour Hadi in Yemen's southern port city of Aden.
The UN Security Council is set to meet on Saturday to discuss a Russian proposal for "humanitarian pauses" in Saudi-led air strikes, which have targeted Houthi rebels over the past nine days.
As the country continued to spiral into chaos on Friday, Houthi fighters and their allies withdrew from Aden's Crater neighbourhood, as well as one of Aden's presidential residences which they had seized a day earlier, residents and a local official said.
Their withdrawal followed clashes and an air strike on the presidential palace at Ma'ashiq, overlooking Crater. At least one Houthi tank was destroyed and another taken over by Hadi's loyalists, they said.
Fighters backing Hadi said they had killed at least 10 Houthis in the clashes in Aden, but did not comment on losses in their ranks.
The Saudi-led coalition dropped weapons and medical supplies to aid pro-Hadi forces in their fight for control of Aden on Friday. The crates of light weapons, telecommunications equipment and rocket-propelled grenades were parachuted into Aden's Tawahi district, on the far end of the Aden peninsula which is still held by Hadi loyalists, Hadi loyalists told the Reuters news agency.
Despite the assistance, pro-Hadi fighters called for further help.
"We urge the coalition to parachute troops on the ground because the strikes from the air and sea won’t be enough," said one fighter, who identified as belonging to the Southern Youth Resistance.
"There must be forces on the ground, the people here are under bombardment... there are deaths, and families remain under siege, we can’t get to them."
Brigadier General Ahmed al-Asiri, a spokesman for the Arab coalition told a news conference air strikes had significantly degraded the Houthi fighters' military capabilities and Hadi loyalists had gained ground in Aden.
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The Saudi-led coalition involves five nations that belong to the Gulf Cooperation Council.
The Houthis are backed in their push by military forces and police loyal to former President Ali Abdullah Saleh.
Houthis advance despite strikes
Despite inflicting heavy losses on the Houthis, the Saudi-led air strikes might not be enough to halt their advance, said Al Jazeera's Mohamed Vall, who has reported extensively on Yemen.
"They [Saudi-led coalition] know they cannot win this war without putting troops on the ground...they are probably waiting for more weakening of Houthi defences [before they do that]," he said.
The UN Security Council will meet to discuss Yemen's crisis at 15:00 GMT on Saturday.
UN aid chief Valerie Amos said on Thursday she was "extremely concerned" about civilian deaths after agencies reported that 519 people had been killed and nearly 1,700 injured in two weeks of fighting.
Also on Friday, al-Qaeda in the Arabian Peninsula, as the Yemen branch is named, consolidated its hold of Mukalla, which they overran on Thursday, seizing its port and a major army base there.
The group has benefited from Yemen's political crisis ever since the Houthis first surged from their northern strongholds last year to seize Sanaa, and much of the north.
|Infographic: Who's for and against military action in Yemen [Al Jazeera]
Source: Al Jazeera and agencies