BAGHDAD — Prime Minister Haider al-Abadi declared Thursday that victory in Tikrit was near and “achieved totally by Iraqi hands” as his troops sought to root out Islamic State militants from their last few footholds in the city.

Islamic State militants still held a sprawling palace complex built by Saddam Hussein and pockets of the city center. But military officials said they were confident that in a few days they would control the entire area, all without direct assistance from American airstrikes.

That would be the most significant defeat for the Islamic State, also known as ISIS or ISIL, since it swept into northern Iraq last June, carving a swath through the country that put the militants a short drive away from Baghdad and, within weeks, brought American forces back into Iraq after they had seemingly marched out for good in 2011.

But that major step for the Iraqi government has come with an emphasis on Shiite militias and Iranian military officials in a leading role. American officials have expressed concerns that the presence of those forces in the Iraqi Sunni heartland could risk the same kind of sectarian alienation that left the country vulnerable to ISIS in the first place.