Ahmed al-Assadi, spokesperson for the second-largest Fateh Alliance list, also denounced "the government's failure to resolve the crisis in Basra".
He said Fatah was "on the same wavelength" as Sairoon and that the pair would work together to form a new government.
The announcement dealt a severe blow to Abadi's hopes of holding onto his post through a bloc - described as the biggest in parliament - unveiled just days earlier.
Al-Abadi said he had instructed security forces to "act decisively against the acts of vandalism that accompanied the demonstrations". Some clashed with security forces, lobbing Molotov cocktails and setting fire to a government building as well as the offices of Shiite militias.
The government has said the protesters' demands are legitimate, while blaming the violence on saboteurs.
Hours before parliament met, four rockets fired by unidentified assailants struck inside the perimeter of Basra airport, security sources said. The U.S. consulate is adjacent to the airport.
Staff at the airport, which is located near the USA consulate in Basra, said flights were not affected.
Passengers are seen at Basra airport after it was targeted by rocket fire.
All operations had been halted since Thursday, after protesters blocked the port's entrance.
On Saturday, a spokesman for an alliance of powerful Shiite militias, many of them backed by Iran, vowed to respond against "those who are carrying out acts of arson and sabotage".
The commander, known as Abu Yasser al-Jaafar, i held a news conference in the city Saturday.
The anger on Basra's streets was "in response to the government's intentional policy of neglect", the head of the region's human rights council, Mehdi al-Tamimi, said.
Angry protesters marched to the city's presidential palaces compound, where Shiite paramilitary troops are stationed, and tried to breach it.
Basra and other cities in Iraq's southern Shiite heartland have been convulsed by the most serious protests in years, with residents complaining of power outages, filthy tap water and soaring unemployment.
Bader said that most of the wounded have received treatment and left the hospitals of Basra province.
The calls for resignation came as the parliament convened earlier in the day for an emergency session to discuss the protests of Basra against water contamination, high unemployment and lack of public services.
The protesters shouted anti-Iranian slogans outside the Iranian Consulate on Friday evening, including "Iran, out, out!" before they stormed it and set a fire inside. Iran and Iraq both strongly condemned the move, raising fears of possible retribution.
At least 30 people have been killed and scores injured since the protests began, according to Iraqi authorities.
The unrest in the south comes amid a political crisis in Baghdad, adding to overall tensions in the country. Iraqi Shi'ite cleric Muqtada al Sadr demanded that top government officials attend a parliament session "no later than Sunday", or face what he called "a popular quake".