A power struggle between Yemen’s internationally-recognized president and his strongman predecessor, Ali Abdullah Saleh, could benefit Houthi rebels who took over the capital, Sana’a, last month.

President Abd Rabbuh Mansur al-Hadi fled to the port city of Aden in February where he established a rival government. Neighboring Arab Gulf states and the United States back Hadi while Iran supports the Houthis, a Shia group from the north of Yemen.

Despite the international support, Hadi’s regime appears to be fracturing. Protests on Thursday called on Saleh to return. At least three people were killed in clashes between Hadi opponents and supporters in Aden.

On Tuesday, Saleh, who was forced to step down in 2012 after more than two decades in power, urged Hadi to resign and go into exile.

“The people can not afford to eat or drink, you have gobbled up their dues, suspended their salaries, brought their livelihoods to a standstill, investment to a halt and tourism too,” Saleh said at a news conference in Sana’a.

The former strongman, who presided over Yemen’s unification in 1990, may not want to return to power himself but rather secure the presidency for his son.

Hadi still has the support of local authorities in the Hadhramaut, Ma’rib and Shabwah provinces which contain most of Yemen’s oil and natural gas reserves. His nephew, Nasser Ahmed, controls security in Aden as well as the nearby Abyan and Lahij regions, both of which are situated in the southwest.

However, Hadi has failed to win over factions that advocate the secession of the former South Yemen. Most of the former North Yemen is controlled by the Houthis.

The Gulf Cooperation Council, a body of Arab kingdoms, called on Thursday for peace talks in Saudi Arabia’s capital, Riyadh. The Houthis as well as Saleh’s General People’s Congress party turned down the invitation.

When asked if the party was colluding with the rebels to undermine Hadi’s government, a spokeswoman said, “The GPC is in harmony with all factions.” She added that “portraying the crisis as being between all political powers and Ansar Allah” — the Houthis’ political wing — “would be a big mistake.”

Tensions between the two strongmen emerged when Hadi purged Saleh’s relatives from the military after taking over in 2012. The latter responded by removing Hadi from the leadership of the ruling party.

Arab Gulf states had forced Saleh to resign that year, fearing that an Arab Spring-style uprising in the country could bring Islamists to power like mass protests had in Egypt. Hadi’s inability to win the loyalty of Saleh’s clan was in part what led him to face the Houthis on his own when they first stormed Sana’a last year.

Only last month did the Houthis dissolve parliament and formally remove Hadi from office. The Gulf Arabs, the United Kingdom and the United States withdrew their ambassadors from Sana’a when Hadi fled to Aden.

The Sunni monarchs in the region see the Shia Houthis as proxies for their nemesis, Iran. The Islamic republic, the Middle East’s largest Shia state, received a delegation of Houthi leaders in Tehran last week. Iranian medical supplies arrived in Sana’a a day after the two regimes had signed an aviation agreement.