TEHRAN/MOSUL, Iraq: Iran has congratulated Iraq on its declared victory over Daesh (ISIS) in Mosul and offered to help rebuild the country, as Iraqi troops push to clear the last of the militants from the devastated city.

"Congratulations to brave people and Government of Iraq upon liberation of Mosul," Foreign Minister Mohammad Javad Zarif wrote late Sunday in a tweet.

"When Iraqis join hands, no limits to what they can achieve."

Prime Minister Haider al-Abadi was in Mosul Sunday, officially marking the end of a difficult campaign to retake the city, where Daesh declared its self-styled caliphate three years ago.

Other Iranian officials were also quick to welcome the victory, Iraq's biggest yet against the militants.

It was a "great achievement in the path to ending the presence and savage actions of the criminal Daesh group against the Iraqi nation", said Ali Shamkhani, secretary of Iran's Supreme National Security Council, in messages to Abadi and Grand Ayatollah Ali al-Sistani, the country's most revered cleric.

"The government, armed forces and the brave nation of Islamic Iran ... are prepared to offer aid to the displaced and injured in the war and help rebuild the cities and vital infrastructure in the country," official news agency IRNA quoted Shamkhani as saying.

Defense Minister Hossein Dehghan and the chief of staff of Iran's armed forces, Major General Mohammad Bagheri, also congratulated Abadi, saying they were ready to boost defence and security ties with Baghdad.

Iraqi forces Monday were pushing to retake the last patch of ground in Mosul where Daesh militants held on to a tiny sliver of the Old City, west of the Tigris River, a day after Abadi's "victory" announcement.

Brig. Gen. Haider Fadhil of the Iraqi special forces says his men, closely backed by U.S.-led coalition airstrikes, are continuing to advance and clear territory in the Old City on Monday.

Iraqi commanders say they believe hundreds of Daesh fighters remain inside the neighborhood and are using their families - including women and children - as human shields.

Iraqi forces launched the operation to retake Mosul last October and began the weeks-long push through the Old City district in June.