BAGHDAD -- More than 2,000 families have fled from the Iraqi city of Ramadi, an official said Thursday, as the Islamic State group advanced on the provincial capital of the western Anbar province, clashing with Iraqi troops.

The extremist group, which has controlled the nearby city of Fallujah for more than a year, captured three villages on Ramadi's eastern outskirts on Wednesday. The advance is widely seen as a counteroffensive after the IS group lost the city of Tikrit, Saddam Hussein's hometown, earlier this month.

Hundreds of U.S. troops are training Iraqi forces at a military base west of Ramadi, but a U.S. military official said the fighting had no impact on the U.S. soldiers there, and that there were no plans to withdraw them.

Sattar Nowruz, from the Ministry of Migration and Displaced, said those fleeing Ramadi 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 said.

Sporadic clashes were still underway Thursday, according to security officials in Ramadi. Government forces control the city centre, while the IS group has had a presence in the suburbs and outskirts for months. They described Ramadi as a ghost town, with empty streets and closed shops.

U.S.-led coalition airstrikes targeted the IS group in Sjariyah, Albu-Ghanim and Soufiya, the three villages the extremists captured Wednesday, the officials added. They spoke on condition of anonymity because they were not allowed to talk to the media.

Anbar's Deputy Gov. Faleh al-Issawi described the situation in Ramadi as "catastrophic" and urged the central government to send reinforcements.

"We urge the Baghdad government to supply us immediately with troops and weapons in order to help us prevent the city from falling into the hands of the IS group," he told the Associated Press in a telephone interview.

Al-Bayan, the Islamic State group's English-language radio station, claimed the fighters were in complete control of at least six areas and most of a seventh to the east of Ramadi since Wednesday, according to the SITE Intelligence Group, a U.S. group that monitors militant websites.

American troops fought some of their bloodiest battles in Anbar during the eight-year U.S. intervention, when Fallujah and Ramadi were strongholds of al Qaeda in Iraq, a precursor to the IS group. Fallujah was the first Iraqi city to fall to the IS group, in January 2014.

Iraqi Prime Minister Haider al-Abadi, who was visiting Washington on Wednesday, made no mention of the events in Ramadi. Instead he spoke optimistically about recruiting Sunni tribal fighters to battle the extremists, saying about 5,000 such fighters in Anbar had signed up and received light weapons.

The IS-run Al-Bayan station also reported that an attempt by Iraqi troops to advance on the Beiji oil refinery in Salahuddin province, about 250 kilometres north of Baghdad, was pushed back and that fighters "positioned themselves in multiple parts of the refinery after taking control of most of it," according to SITE.

Iraqi officials could not immediately be reached for comment on the fighting around Beiji. On Monday, Oil Minister Adel Abdul-Mahdi said that Iraqi forces, backed by U.S.-led coalition airstrikes, had repelled an IS attack on Beiji over the weekend.

Meanwhile, a senior U.S. military official told The Associated Press that there were no plans to evacuate U.S. troops from the Ain al-Asad air base, about 110 kilometres west of Ramadi -- and stressed that the current fighting around Ramadi had no impact on the base. He spoke on condition of anonymity because he was not authorized to talk to the media.

Since January, hundreds of U.S. forces have been training Iraqi troops at the base. An attack on the base by a suicide bomber in February was repelled.