BAGHDAD — Nouri al-Maliki’s decision to step down as Iraq’s prime minister raised hopes Friday for a new government that can roll back an increasingly powerful Sunni insurgency and prevent the country from splitting apart.

But to do that his successor has to unify Shiite, Sunni and Kurdish factions that deeply distrust each other and have conflicting demands, all while dealing with a humanitarian crisis and the extremists’ continuing rampage in the north.

The man tapped to become the next prime minister, Haider al-Abadi, a veteran Shiite lawmaker, faces the immense challenge of trying to unite Iraqi politicians as he cobbles together a Cabinet in just over three weeks.

Al-Abadi said Friday his government will be based on “efficiency and integrity, to salvage the country from security, political and economic problems” – but that is easier said than done in a country where forming a government often falls victim to roadblocks and infighting.

Sunni politicians are pressing for greater political influence, saying their disenfranchisement under al-Maliki’s Shiite-dominated government fueled support among the Sunni minority for the insurgency, led by the extremist Islamic State group. At the same time, the military needs significant bolstering after falling apart in the face of the militants’ advance and proving incapable of taking back lost territory.

“Sunnis and Kurds were present in the Maliki government, but rarely included in the key decision-making process,” said retired Brig. Gen. Mark Kimmett, former military spokesman for coalition forces in Iraq. “One hopes that al-Abadi understands that inclusion has to be more than mere participation.”

Many Iraqis expressed a sense of relief Friday that al-Maliki had relented after weeks of insisting on a third four-year term, fueling a political crisis that raised fears of a coup in a country with a long history of violent power grabs.

During Friday prayers in Baghdad’s Shiite Sadr City district, a man distributed sweets to Shiite worshippers, proclaiming, “Saddam has been brought down.”

The comparison of al-Maliki to the late dictator Saddam Hussein showed the depth of opposition to the outgoing prime minister even among some of his fellow Shiites. Sadr City is dominated by followers of powerful Shiite cleric Muqtada al-Sadr, one of al-Maliki’s harshest critics. Six years ago, al-Maliki sent security forces to battle al-Sadr’s militias to establish his authority and project his image as a national leader.

“We congratulate the Iraqi people for the victory that has been done this week. It is the week of congratulations,” said Ali Talaqani, a preacher loyal to al-Sadr, in his sermon to Sadr City worshippers.

Shiite factions turned against al-Maliki largely because they saw him as a domineering leader who monopolized power and allowed widespread corruption. Critics say he staffed the military’s officer corps with incompetent loyalists, playing a major role in the army’s collapse in the face of the Islamic State militants over the past two months.

Sunni factions also accused him of widespread corruption. But their principle grievance was that his government sidelined their community, carrying out sweeping arrest raids and violently dispersing protests.

“We are ready to cooperate with al-Abadi to make him succeed in his mission on the condition that the demands of our Sunni people are met,” Ahmed al-Misari, a Sunni lawmaker, told The Associated Press.