However Iraqi political and military officials had vowed that victory would be declared by the end of 2016.
The militants said they had been targeting an Iraqi army position.
He also voiced Iran's readiness for helping the regional nations and governments until full eradication of the remnants of terrorists.
The two bombers hid among a group of civilians picking their way through the devastated area around mostly destroyed mosque, targeting Iraqi troops.
Issuing a statement on Sunday 160 Iranian parliamentarians offered their congratulations to the Iraqi people and government as well the Islamic Revolution Guards Corps' (IRGC's) advisory mission in the Arab country over the recent liberation of Mosul.
The US-backed operation to retake the city was launched last October and has lasted nearly nine months.
Iraqi forces had been closing in on the Old City in west Mosul for months, but its narrow streets and closely spaced buildings combined with a large civilian population made for an extremely hard fight.
"Iraqi forces are advancing into the Old City", Yahia Rasoul, Iraqi joint forces spokesman, told state-run TV on Saturday, using the Arabic acronym for ISIL, also known as ISIS.
Iraqi forces surround Islamic State in Mosul
Those who escaped on Friday streamed through alleyways near the Grand al-Nuri Mosque, which Islamic State fighters blew up a week ago.
At least 50,000 civilians, about half of the Old City's population, are believed to still be trapped in ISIL-held pockets of Mosul.
Highlighting the major security challenges Iraq would face after Mosul, a suicide bomber attacked a camp for displaced people west of Baghdad on Sunday, killing 14 people and wounding 13, a police major and a doctor said.
Iraq's Prime Minister declared an end to the IS caliphate in June after Iraqi forces reclaimed the landmark al-Nuri mosque in the Old City and pledged victory was 'near'.
Iraqi forces on Monday recaptured new areas in the remaining redoubt of Islamic State (IS) militants in Mosul's old city amid fierce clashes that left dozens of IS militants killed, the Iraqi military said.
Fighting remained intense, however.
The Islamic State, however, is far from giving up in other points of conflict.
The attack has not been claimed in the immediate future, but it is reminiscent of the mode of operation of the AES who still control areas of this vast province.More news: At the White House, women employees are getting paid lesser than men
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