A crucial question is how Sunnis in Iraq will react to seeing some of their top officials — including the Sunni vice president, Osama al-Nujaifi, and a Sunni deputy prime minister, Saleh al-Mutlaq — removed from office. The posts were largely ceremonial, but they came with large budgets that allowed the officials to reward their constituencies with patronage jobs.

The elimination of sectarian and party quotas in filling high-level posts may also alienate Sunnis if, in practice, the new policies lead to further dominance by Shiites.

“I think that the decision of Abadi will lead to the anger of the Sunni community, because the Sunnis see the positions of deputy prime minister and vice president as their entitlement,” said Hadi Jalo Marie, who participated in the protests and is the head of the Journalistic Freedoms Observatory, a Baghdad advocacy group. “So I think that Sunnis will see that Abadi’s decision represents a continuation of the marginalization of the Sunni sect.”

In addition to Mr. Maliki, two other figures who have been prominent since Saddam Hussein was overthrown will now be out of government: Mr. Nujaifi and Ayad Allawi, a Shiite and former prime minister whose Sunni-dominated bloc won the most parliamentary seats in the 2010 national election. Both men have voiced broad support for Mr. Abadi’s proposals, while warning that eliminating their posts may be unconstitutional.

Mr. Allawi said on Monday that he would wait to see if the measures worked as intended, but not for long. “I will give three months to carry out the reforms,” he said. “Otherwise, we will call the Iraqi people to demonstrate, and we will call for new elections to overthrow the government and bring in new people to serve the society and to solve the corruption crisis in the country.”

Iraq’s Sunni leaders, including the speaker of Parliament, Salim al-Jubouri, have largely supported the measures, but it is an open question how ordinary Sunnis — many of whom live in territory controlled by the Islamic State, also known as ISIS, ISIL or Daesh — will feel about them. The Islamic State was able to capture large stretches of territory last year in part by capitalizing on the grievances of Sunnis who felt marginalized under Mr. Maliki’s rule. Some analysts have said the group could exploit Mr. Abadi’s measures by arguing that they further disenfranchise Sunnis.

At the same time, the changes could “cut the Sunnis out of a major part of the patronage system,” said Ramzy Mardini, an Iraq expert and nonresident fellow at the Atlantic Council, a research group in Washington.