PanARMENIAN.Net - Iraq's armed forces pressed on with their offensive to retake the city of Fallujah from Islamic State on Tuesday, June 21dislodging the militants from two eastern districts and pushing them back into a handful of northern and western neighborhoods, Reuters reports.

A military statement said the elite counter-terrorism forces took the northeastern Shurta police district while units from Baghdad operations command recaptured the Askari military neighborhood.

Islamic State still held the northern districts of Jughaifi and Golan as well as the western banks of the Tigris river.

Fighting to recapture the Iraqi city longest held by Islamic State, now in its fifth week, has forced more than 85,000 residents to flee to overwhelmed government-run camps.

Prime Minister Haider al-Abadi said last week that the recapture of Fallujah would pave the way for the military to march on Mosul, Islamic State's de facto capital, Reuters says.

The operation's commander Lieutenant General Abdul Wahab al-Saidi told Reuters on Monday that U.S.-backed Iraqi forces expected the final push would take place in the west.

The Iraqi army is also pressing on with an offensive to dislodge the militants from farmlands located on the western bank of the Euphrates, opposite the built-up area of Fallujah, that the militants use as a base for snipers and mortar attacks.

"The simultaneous attacks are continuing from four directions to tighten the noose around Daesh (Islamic State)fighters entrenched in houses among civilians and prevent them from catching their breath," said Colonel Ahmed al-Saidi from the federal police.

Government troops launched the operation on May 23 to retake Fallujah, a bastion of the Sunni Muslim insurgency against U.S. forces that toppled Saddam Hussein, a Sunni, in 2003, and later against Shi'ite-led governments.

The militants seized Fallujah in January 2014, six months before they declared a "caliphate" over part of Syria and Iraq.