BAGHDAD — Iraqi government forces and allied militias took control of the western neighborhoods of Tikrit on Thursday, military officials said, leaving only one area, including a palace complex once used by Saddam Hussein, in the hands of Islamic State militants.

Military officials said they were confident of declaring victory within a few days in Tikrit, a central objective in rolling back the militants and the government’s largest operation against the Islamic State since it swept into much of the country’s north and west in June.

Top Iraqi officials, including Prime Minister Haider al-Abadi, visited troops near the front lines on Tuesday night and Wednesday. They called for security forces to facilitate the return of displaced civilians from Tikrit and surrounding areas.

Bringing civilians back without revenge attacks or continuing conflict will be the next test for Iraq’s government if it holds its gains and completes the operation in Tikrit. The government mustered a 30,000-strong force, the bulk of it fighters from Shiite militias, in an effort to retake the city.

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The fight for Tikrit has added emotional resonance. It was there that Islamic State fighters massacred more than 1,000 Shiite soldiers from the Camp Speicher base last year, and many Shiites accuse some local Sunnis of taking part.

Raw emotions were on display in Baghdad on Thursday morning, where several dozen parents of the dead soldiers gathered at the busy Tahrir Square, holding photographs of their sons and calling for an international investigation into the deaths, saying they did not trust Iraqi officials to arrive at the truth.

They said they were happy to see the Islamic State falling in Tikrit, but their anger and grief were not assuaged. They placed blame for the massacre not only on the militants but also, in apparently equal measure, on what they said was the cooperation of Sunni tribal leaders and the negligence and corruption of Iraqi officials and their sons’ commanders.

“We want a legal trial to bring justice for our sons,” said one father, Mahdi Saleh, clutching a picture of his 22-year-old son, Nahum. Standing beside Mr. Saleh, another man who lost a son, Ali Shadhan Shahrar, demanded that the perpetrators be “executed in front of the victims’ families.”

“We have no problem with the Sunnis, and we will have unity,” Mr. Saleh added. “But peace with those criminals? Never ».

The government advances in Tikrit came as reports surfaced of new abuses by both Iraqi security forces and the Islamic State, also known as ISIS or ISIL.

Iraqi officials said they would investigate reports of atrocities, filmed and posted in recent months on social media, and committed by armed men in uniforms with the insignia of a special forces unit and other regular government forces.

The images have been circulating on social media, and they were compiled and presented to Iraqi and United States officials by ABC News. The images raised the question of whether Iraqi forces ran run afoul of a measure that requires the United States government to cut off aid to foreign militaries that commit human rights abuses.

One video shows what appears to be a 12-year-old boy being shot to death in the street after being accused of working with the Islamic State. Another shows two civilians being shot after insisting that they were not involved with the militant group; fighters then riddle their bodies with bullets. Another apparently shows a civilian being beheaded, and other images show a head propped on the front bumper of a military vehicle that appears to be an American-made Humvee.

Iraqi officials have showed footage to the BBC that they said proved that the Islamic State was using chlorine gas in roadside bombs. The images show orange clouds rising from the bombs as Iraqi ordnance disposal teams detonate them. Chlorine, while not as dangerous as substances like sarin, banned by international treaty, can cause coughing and burning eyes and in close quarters can be fatal.

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During the past week of battle, military officials in Salahuddin Province said dozens of residents of the city of Samarra, near the front lines but not part of the fighting, were sickened when a bomb containing chlorine exploded in a pile of garbage.

Iraqi officials said two mass graves discovered in Tikrit, believed to be Speicher victims, would be excavated methodically.

A militia leader told Iraqiya state television that another grave had been found, which he said appeared to be holding recent, hastily buried Islamic State casualties of the current battle.

Mr. Abadi was joined on his visit to the front by Nuri Kamal al-Maliki, the former prime minister who was in office when the Islamic State took over Tikrit and was later pushed out amid allegations that his sectarian policies had created fertile ground for the militants.

Mr. Maliki thanked all the groups fighting the militants. And, in acknowledging the role of the federal police in the battle, Mr. Maliki seemed to recognize the shortcomings of the force under his authority, when many units fled their posts in the face of the Islamic State advance, as well as its apparent improvement.

“The federal police of today is not like before,” he said.

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