— Shiite rebel forces backed by tanks and heavy machine guns pushed deeper into Yemen’s second-largest city on Wednesday in a bid to strengthen their hold even as Saudi-led airstrikes attempt to cut off their supply lines and cripple their capabilities.

The showdown over Aden, a key port and gateway to Yemen’s south, underscores the imperatives on both sides in the widening conflict — in which Saudi Arabia and its Arab allies have launched a campaign to beat back the rebels, thought to be backed by Shiite power Iran, and block a perceived bid by Tehran to expand its influence.

The rebels, who control Yemen’s capital, Sanaa, hope to find new defensive positions and open fresh supply channels by taking full control of Aden. The Saudi-led alliance, meanwhile, is trying to hang on to the city but is wary about carrying out airstrikes in populated areas for fear of civilian casualties.

Earlier Wednesday, more than two dozen workers were killed when explosions destroyed a dairy plant in the Yemeni port city of Hodeida. There were conflicting claims of responsibility.

In the Saudi capital, a military spokesman said the Shiite rebels, known as Houthis, attacked the facility, which is near a military base. Brig. Gen. Ahmed Asseri said he based the assertion on “intelligence” sources in Hodeida. He did not clarify but has said previously that Yemeni soldiers were helping alliance warplanes target rebel sites.

Some residents in Hodeida, however, said it appeared that an airstrike hit the dairy plant.

Taher Mohammed Almaamari, the deputy manager at the Health Ministry office in the city, said that at least 29 people were killed and more than 200 injured.

Other reports gave higher death tolls. The Associated Press, citing local officials, said at least 35 people were killed, which would place the attack among the single bloodiest for civilian casualties in Yemen since the airstrikes began last week.

It follows accounts by aid groups of increasing civilian deaths in the air campaign against the Houthis. Saudi Arabia and its partners want to reinstate President Abed Rabbo Mansour Hadi, who fled Yemen last week in the face of a rebel advance on his compound in Aden.

The city appeared closer to falling into rebel hands after Wednesday’s gains. Houthi fighters — joined by soldiers loyal to former president Ali Abdullah Saleh — faced barrages from a warship while on a coastal road but managed to reach areas near the center of Aden with tanks and vehicles mounted with heavy machine guns. At least some of the rebel forces entered the vacated Russian Consulate, said Anis Mansour, editor of the Huna Aden news Web site.

It was unclear how many ground forces loyal to Hadi remained to defend Aden.

Abdulnaser Abdulqawi Alarabi, 46, a lawyer and resident of Aden’s Khor Maksar district, described rebel tanks and snipers firing at random. Shelling destroyed his car and damaged his home, he said. His family huddled in the corner of the living room on the second floor, he said. Another shell hit the first floor.

“It was a horrifying experience, and we felt that the minutes were like days,” Alarabi said.

The family fled in a neighbor’s car during a lull in the violence.

Meanwhile, the evacuation of foreign workers moved ahead. An Indian navy vessel carried nearly 350 Indians from Aden to the African nation of Djibouti late Tuesday.

In New York, UNICEF said 62 children had been killed in the Yemen unrest over the past week, and U.N. Secretary General Ban Ki-moon reminded all sides in the war of their “obligations under international humanitarian law” to avoid civilian deaths. A report by the rights group Amnesty International said that at least six civilians, including four children, were among the dead in a raid targeting a suspected Houthi checkpoint early Tuesday.

In Riyadh, Saudi Arabia, Asseri said forces are “doing everything they can” to avoid civilian casualties. But he said the rebels have increasingly shifted into residential areas to hide from airstrikes.

“They are inside the villages and towns as part of their strategy,” the spokesman said.

Saudi Arabia has massed ground troops along its southern border with Yemen, but Asseri said there were no imminent plans to move into Yemen.

Saleh denies accusations that he has aided the Houthis, and he has blamed Yemen’s instability on Hadi. Saleh could not be reached for comment on Wednesday. Houthi leaders also deny any collusion with him.

Diplomats and analysts say, however, that coordination between Saleh and the Houthis was crucial for the Houthi takeover of Sanaa in September. They say Saleh called on loyal officers to stand down, allowing the rebels to swiftly capture the capital.

In November, the U.N. Security Council slapped sanctions on Saleh, charging that he was threatening Yemen’s stability and undermining a political transition away from his rule. Diplomats and analysts say he has turned to his vast wealth, accumulated during his three-decade rule, to undermine Hadi. A recent U.N. report says he may have amassed as much as $60 billion in that time — a sum roughly equal to Yemen’s annual gross domestic product.

A leading political analyst in Sanaa said the Saudi assaults have begun to stir sectarian sentiment, pushing Saleh and the largely northern Zaydi tribes, including the Houthis, closer together. Saleh, 73, is a Zaydi Shiite from the north, where there is resentment at the predominantly Sunni south, which used to be a separate country until 1990. A civil war in 1994 was won by Saleh’s forces, which defeated southern separatists.

But signs of discord are emerging between Saleh and the Houthis. Last week, in a televised address, he pleaded for a truce with Saudi Arabia.

Rebel officials were furious.

“Saleh is only doing this to keep his relationship with Saudi and the gulf states friendly, because he wants, above anything else, to protect his personal interests,” said Deif Allah al-Shami, a member of the Houthi political bureau.

Murphy reported from Riyadh. Hugh Naylor in Beirut and Erin Cunningham in Cairo contributed to this report.

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