The reports come after the deputy head of the Anbar Provincial Council, Falih Essawi, warned that Ramadi could fall to the ISIS militants within hours.
The Iraqi security forces backed by Albu Nimr tribe killed 11 ISIL terrorist in al-Khasfa area in Haditha city in Western Anbar on Wednesday night.
Head of the Iraqi Parliament's Security and Defense Committee Hakem al-Zameli said the situation in Anbar province is under control, adding that the US-led coalition has refrained from conducting airstrikes on ISIL positions in Anbar despite Iraq's repeated requests.
Hakem al-Zameli said dismissed media reports claiming that ISIL terrorists made gains in the province as an ISIL attempt to break the Iraqi forces' morals.
He also condemned the position of the US-led coalition, saying the coalition has not conducted any airstrikes against ISIL positions despite Iraqi requests.
According to some media ISIS recently took control of areas near Ramadi, which is only about 70 miles (113 kilometers) west of Baghdad and is the capital of Iraq's vast Anbar province, the country's Sunni heartland. The advance by the extremist group has forced thousands of civilians to flee east to Baghdad.
Clashes between Iraqi forces and ISIS militants pressing their offensive for Ramadi, has forced more than 2,000 families to flee from their homes in the area, an Iraqi official said Thursday.
Sattar Nowruz, from the Ministry of Migration and Displaced, said that the over 2,000 families that fled Ramadi were in a "difficult situation" and have settled in southern and western Baghdad suburbs.
Tents, food and other aid are being sent to them, he said. The ministry is also assessing the situation with the provincial government in order "to provide the displaced people, who are undergoing difficult conditions, with better services and help," Nowruz added.
It is reported that ISIS militants captured three villages posing a major threat to the city by the militants to date.
The fighters seized the villages of Sjariyah, Albu-Ghanim and Soufiya, which had also been under government control until now, and residents said they had to escape their homes.