Smoke billows from a car parts store hit by shells Wednesday during the conflict in the Yemeni port city of Aden. (Fawaz Salman/Reuters)

The three-year-old Yemen conflict has largely been cast as a war that pits an internationally recognized government against Iranian-backed rebels who ousted it from the capital and now also control much of the north.

But fighting in the southern Yemeni city of Aden over the past week revealed the extent to which Yemen's war also is driven by other historical grievances that could pose serious obstacles to negotiating an end to the conflict, according to Yemeni and Western analysts.

Over several days, southern separatists battled their estranged partners — forces loyal to ousted President Abed Rabbo Mansour Hadi — and briefly seized control of Aden. Both sides belong to the same alliance led by Saudi Arabia and the United Arab Emirates, which is fighting the Iranian-backed Houthi rebels in an effort to restore Hadi to power.

The battles in Aden have exposed the fragility of that alliance and highlighted the diverging agendas of Saudi Arabia and the United Arab Emirates.

The separatists, known as the Southern Transitional Council (STC), have long sought to restore the independent state of South Yemen, which existed before Yemen was unified in 1990. They have long been suspicious of the northern-based central government in Sanaa, which Hadi presided over, accusing it of corruption and undermining the south.

The violence, said analysts, is a reflection of these long-simmering tensions.

"It shows how the war has shattered the country, fracturing it along historical divides," said April Longley Alley, a senior Yemen analyst for the International Crisis Group. "The narrative of a 'legitimate government' fighting the 'Iranian-backed Houthis' obscures a complex local reality, and it hinders efforts to achieve peace."

The infighting within the alliance intensified the despair in the Middle East's poorest nation. More than three dozen people died in last week's clashes, adding to the war's death toll of more than 10,000, mostly civilians killed by Saudi-led coalition airstrikes. Millions more are suffering from hunger and disease in what aid agencies describe as one of the world's most dire and forgotten humanitarian crises.

Yemen's war began in the spring of 2015, after the Houthis seized the capital, Sanaa, and forced Hadi and his government to flee south to Aden. Saudi Arabia and other Sunni Muslim countries entered the conflict largely to prevent their regional rival, Iran, a Shiite Muslim theocracy, from projecting its influence along their borders by backing the Houthis.

Hadi had come to power after his predecessor, Ali Abdullah Saleh, who ruled the country for more than three decades, was himself forced to step down after a populist revolt, part of the Arab Spring uprisings. When Hadi was chased out of Sanaa, he set up a government in exile in Aden with the backing of the Saudis and Emiratis, even though he has presided mostly from the Saudi capital, Riyadh.

Many southerners had expected the Hadi government to improve their lives. But over the past three years, Hadi has struggled to exert political authority or bolster the economy. Aden has been shaken by suicide bombings and other violence, staged by al-Qaeda's Yemeni branch as well as by a nascent Islamic State affiliate.

"Very little has been done to stabilize the situation and get things working again," said Gerald Feierstein, a former U.S. ambassador to Yemen. "People have gotten increasingly frustrated there."

The trigger for the past week's clashes was the expiration of a deadline set by the separatists for Hadi to dismiss his government. They accused the government, run day-to-day by Prime Minister Ahmed Obaid bin Daghr, of corruption and mismanagement. After the separatists took control of much of Aden, Hadi's officials were confined inside the presidential palace, and some contemplated fleeing the city.

Amid these divisions in the alliance, there are "real questions about the viability or the credibility of the Hadi government and what exactly do they represent sitting at the other side of the table," said Feierstein.

"These are the kinds of issues that are going to make rebuilding Yemen difficult," he added. "In the immediate term, it complicates efforts to revive the political process."

Further imperiling the chances for a political settlement is a separate set of divisions within the Iranian-backed alliance. Late last year, the Houthis had a falling out with the influential former president Saleh, who had aligned himself with them, and they killed him. That raised questions about whether the Houthis have the desire or will to negotiate an end to the conflict.

A day after the southern separatists surrounded the presidential palace in Aden, Saudi Arabia and the UAE sent delegates to defuse the animosities and put in place a cease-fire.

Saudi Arabia is the main backer of the pro-Hadi forces. The UAE is the main supporter of the separatists, training them and working closely with them in fighting the Houthis and Islamic extremists.

Saudi Arabia and the UAE have other differences as well. Saudi Arabia, Alley said, is closely aligned with an influential Yemeni party, Islah, which has historical links to the Muslim Brotherhood. (The party recently announced that it had severed links to the Brotherhood.) The UAE, for its part, opposes Islah.

Despite the tensions, it is highly unlikely that Saudi Arabia and the UAE will part ways over Yemen. Both countries share the belief that the Houthis and Iran pose an existential threat to the region.

The southern separatist group, Alley added, "is on a collision course with the pro-unity Hadi government and has been for some time. Now what we see is the UAE and [Saudi Arabia] scrambling to paper over differences between the two so that they can maintain, at least while the war with the Houthis continues, the myth of a unified front under an internationally recognized government."

In Aden, many residents view the UAE's growing presence suspiciously and worry the country could seek economic gain by trying to control Yemen's ports, especially Aden, which is nestled beside key shipping lanes.

"The Emirates has ambitions in the south, and one of its most important ambitions is the port of Aden," said Hassan Aljalal, a Yemeni journalist. "And its support for the southern movement shows this ambition."

Hesham Alghannam, a Saudi researcher at the University of Exeter, said Yemen's exiled government shared some of the blame for the violence in Aden, and should "submit its resignation if it is unable to manage the battle against the Houthis and provide services to the citizenry at the same time."

The authorities had received several billion dollars of aid from the Saudi-led coalition, and "where did the money go?" Alghannam said. The coalition, he added, also needed to put more pressure on the government to "deliver for the people."

As for the southerners and their hopes for independence, "they must wait until things become clear," Alghannam said. Despite their apparently conflicting approaches to the south, the UAE and the Saudis were in agreement over the need to tamp down any moves toward secession, he said.

"You cannot start another war in the south. It would be a contradiction for the Arab coalition," he said, adding that, by resorting to violence, the pro-secession forces were, "knowingly or not, serving the Houthis."

Kareem Fahim contributed to this report from Riyadh.