The Houthi forces have been battling to take Aden, a last foothold of fighters loyal to Saudi-backed President Abd-Rabbu Mansour Hadi, advancing to the city center despite 11 days of air strikes by a Saudi-led coalition of mainly Gulf air forces.
Sunni Muslim Saudi Arabia launched the air strikes on March 26 in an attempt to turn back the Iran-allied Shi'ite Houthis, who already control Yemen's capital Sanaa, and restore some of Hadi's crumbling authority.
The air and sea campaign has targeted Houthi convoys, missiles and weapons stores and cut off any possible outside reinforcements - although the Houthis deny Saudi accusations that they are armed by Tehran.
The fighting has failed so far to inflict any decisive defeat on the Houthis, or the supporters of former president Ali Abdullah Saleh who are fighting alongside them, but the growing death toll and humanitarian suffering has alarmed aid groups.
The United Nations said on Thursday that more than 500 people had been killed in two weeks of fighting in Yemen, while the International Committee of the Red Cross has appealed for an immediate 24-hour pause in fighting to allow aid into Yemen.
The ICRC, which has blamed the Saudi-led coalition for delays in aid shipments, said it received approval to fly in medical supplies and staff and hoped to send two planes on Monday.
A spokesman for the military coalition said the ICRC had approval to fly in aid on Sunday but pulled out because of problems with the company from which it chartered a plane.
Brigadier General Ahmed Asseri also said a Sudanese flight was prevented from landing at Sanaa on Sunday by authorities in the Houthi-run capital, and a Turkish evacuation flight was held up. "Usually, the delay is because of the other side," he said.
A pro-Hadi militia source said 36 Houthi and allied fighters were killed on Sunday in Aden's central Mualla district, near the port, while 11 of Hadi's combatants died.
Houthi forces initially advanced towards the port area, but hours later had been pushed back several streets towards an army base.
"There are bodies in the streets and we can't get close because there are Houthi snipers on the rooftops. Anything that gets near they shoot at, and the shelling on Mualla has been indiscriminate," a medic told Reuters.
Asseri said the coalition was providing pro-Hadi fighters with intelligence, equipment and logistics. "We hope in a few days they will control most of the city," he told reporters in Riyadh.
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