A U.S.-backed Syrian coalition of Kurdish and Arab fighters has launched an offensive to begin forcing Islamic State of Iraq and Syria (ISIS) fighters from the de-facto capital city of their self-proclaimed Islamic "caliphate" -- or at least to begin doing so.

The Syrian Democratic Forces, or SDF, as the umbrella group of fighters is called, announced the move on Twitter, and it was soon reported on Kurdish media and confirmed to CBS News by a representative for the group.

SDF statements posted on the group's official Twitter account said the operation was focused on liberating northern Raqqa, to protect the largely-Kurdish areas to the north from ISIS attack.

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Early reports of casualties all centered in the rural area to the north of the city.

ISIS has controled Raqqa in northern Syria since sweeping across vast swathes of that country and neighboring Iraq in 2014. It is believed to operate most of its administration and control and command from the city.

A map shows the areas controlled by ISIS as of October 2015. The group's territory has shrunk considerably since then, but it remains entrenched in Raqqa, Syria, its de-facto capital, Iraq's 2nd largest city of Mosul, and other smaller cities and towns. CBS

It was not immediately clear how far the SDF hoped to push into Raqqa proper -- or how quickly, but a commander with the Kurdish YPG militia, which is taking part in the operation, said the operation launched Tuesday was a necessary first step to reclaim the city.

He told CBS News the SDF fighters needed to focus on clearing the area to the north of the city of ISIS militants, and then hold that ground before launching a wider attack on the heart of ISIS-held Raqqa.

U.S. officials have indicated to CBS News that the push announced by SDF likely does not amount to a concerted effort to retake the entire city, yet. The task is too large for the SDF on its own, and there is no indication, in spite of SDF claims of backing by the U.S.-led coalition, that a significant international operation is under way.

Raqqa sits only about 50 miles south of Syria's border with Turkey, in land long-dominated by Kurds.

"#Raqqah Liberation Brigade and the @CJTFOIR forces will accompany #SDF during the campaign," Rojda Felat, Democratic #Syria Forces Comm. — QSD Press Office (@QsdPress) 24 May 2016

In a message posted to its official Twitter account, the SFD said members of the U.S.-led anti-ISIS coalition, dubbed "Operation Inherent Resolve," would "accompany" SDF forces on the offensive.

Operation Inherent Resolve has largely consisted, from the U.S. standpoint, of airstrikes against ISIS positions in both Syria and Iraq. Pentagon officials would not comment on any level of involvement by Operation Inherent Resolve or the U.S. military in or around Raqqa.

About 200 U.S. troops are in Syria in a training capacity.

On Monday, the army in Iraq announced a large-scale offensive to reclaim Fallujah from ISIS. The city just 40 miles west of Baghdad has been a stronghold of the militants in that country since January 2014. It is among the top prizes for Iraqi troops and their U.S. backers, but Mosul, the second-largest city in Iraq, remains the extremists' most valuable enclave in that country.

Russian Foreign Minister Sergey Lavrov said Tuesday that Moscow was ready to coordinate with the U.S. and the Kurdish forces on the ground for the offensive on Raqqa.

Americans advisers have been trying to pull together enough local fighters to capture Raqqa, the main prize in northern Syria, for weeks. Raqqa already is largely isolated, and there had been signs that ISIS feared an imminent offensive.

The American Central Command chief, Army Gen. Joseph Votel, paid a secret visit to northern Syria on Saturday to personally take account of the U.S. mission to shore up the SDF. He was the most senior U.S. commander to enter Sryia since the U.S. began its operations against ISIS in 2014.

The U.S. has organized fighters from a wide array of different groups into the umbrella SDF. It is comprised mostly of Syrian Kurds, numbering at least 25,000 fighters, with a smaller element of Syrian Arabs numbering perhaps 5,000 to 6,000.

One U.S. adviser training the SDF in northern Syria estimated that at least 6,000 to 10,000 fighters would be needed for a Raqqa offensive.

In announcing the offensive on Tuesday, the SDF claimed as many as 50,000 had been mobilized, and called on anyone else in the area to come out in support.

The U.S. strategy relies on training, organizing and advising local fighters for such combat, rather than committing American forces.

That has proven to be a slow approach, subject to much criticism in Congress. It is based on a belief that the locals are best able to sustain a lasting defeat of the militant group.

Votel, who inherited the strategy when he took over Central Command in April from the plan's main military architect, Gen. Lloyd Austin, said in an interview that he believes it is working.

The key, he said, is tailoring U.S. support for the local Arab, Kurd and other local fighters so that they can do things their own way, "not trying to replicate how we would do things."

"It may not be the exact way we would do something in the American army or a Western military force, but the approach they take works for them. That's what's important," he said.