Baghdad (CNN) -- ISIS fighters stood Saturday on the verge of taking not just a key Syrian town along the Turkish border, but also an entire province on Baghdad's doorstep -- spurring leaders of that province to urgently plead for U.S. ground troops to halt the Islamist extremist group's rapid, relentless assault.

The situation in Anbar, just to the west of Baghdad, is "very bad," said Sabah Al-Karhout, the president of Anbar Provincial Council.

ISIS, the self-proclaimed "Islamic State" which also is referred to as ISIL, controls about 80% of the province. Reports Saturday suggest they have encircled Haditha, the last large town in Anbar province not yet in the militants' hands.

Should all of Anbar fall, the Sunni extremists would rule from the perimeter of Iraq's capital to Raqqa in Syria (at least), according to the provincial council's deputy head, Falleh al-Issawi.

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To stave off Anbar's collapse, provincial leaders have asked Iraq's central government to intervene immediately and for U.S. ground forces to be deployed there, said al-Issawi.

Iraqi army forces and Anbar tribesmen fighting alongside them have threatened to abandon their weapons if the U.S. military does not intervene to help them, he said, because they are faltering before the ISIS onslaught.

The army soldiers are not capable of defending themselves against ISIS because of a lack of training and equipment, he said. Already, some 1,800 tribesmen in the province have been killed or injured in the struggle.

The Iraqi government has been adamant that it does not want U.S. forces on the ground, and President Barack Obama has not shown any intent to deploy any.

The Iraqi government said it has not received any official request from Anbar province for U.S. military intervention and ground forces to help in the fight against ISIS, Prime Minister Haidar al-Abadi's media office said Saturday.

"If we receive any request, we will look into it and we will give our recommendation, but thus far we have not received any request," the office said.

A U.S. defense official said Saturday that Iraq's government hasn't asked for any more American troops beyond those already in Iraq.

And if they did, the official added, "The U.S. will not deploy combat ground forces to Iraq. And we remain focused on enabling the (Iraqi military) in the fight against ISIL through our advise/assist efforts and the air campaign."

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The air campaign this official referred to resumed Saturday. A coalition airstrike killed more than 30 suspected ISIS militants who were part of an armed convoy heading toward the Ein al-Assad military base west of Ramadi, said town police Capt. Bahjat al-Hamdani.

Such airstrikes have been going on since August, a stretch in which ISIS has expanded its reach.

In Iraq, the group appears to be targeting cities along the Euphrates River. Al-Karhout said his provincial council has intelligence that ISIS has dispatched as many as 10,000 fighters to Anbar from Syria and Mosul in northern Iraq.

U.S. Defense Secretary Chuck Hagel acknowledged the dire situation Friday, telling reporters, "Anbar province is in trouble. We know that."

A senior U.S. defense official also told CNN that Iraqi forces are "up against the wall" in Anbar. Some units are in danger of being cut off by the advancing militants, who say they are members of ISIS.

The Iraqis' ultimate goal is to take back some of the vast areas, in both Iraq and Syria, that ISIS controls.

But right now, Iraqi forces appear to be mostly trying to survive, taking defensive positions and using Apache helicopters again, even after two were shot down in the area this week, according to the U.S. official.

But officals said Baghdad is not likely to be the next domino to fall.

A U.S. Central Command official said Saturday there are "pockets" of the militant group's fighters around the capital, but "no imminent threat of an effective ISIL offensive."

Hagel said Saturday, while addressing reporters in Chile: "Iraqi security forces are in full control of Baghdad."

Still, the equation could change if ISIS threatens Baghdad airport, from which U.S. Apache helicopters operate.

Retired U.S. Air Force Lt. Col. Rick Francona, a CNN military analyst, said: "I think at some point, there's going to be the need for an additional ground force in western Iraq."

Those troops could be American or could be provided by other coalition nations, he said, but the Iraqi army, even after coalition airstrikes, has not been able to blunt the momentum of ISIS.

"The Iraqi army has virtually evaporated. The command structure doesn't exist. Although they have some good soldiers, they have no leadership. So, additional ground forces are going to be necessary."

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