Money flows to the group, the Nusra Front, from like-minded donors abroad. Its fighters, a small minority of the rebels, have the boldness and skill to storm fortified positions and lead other battalions to capture military bases and oil fields. As their successes mount, they gather more weapons and attract more fighters.

The group is a direct offshoot of Al Qaeda in Iraq, Iraqi officials and former Iraqi insurgents say, which has contributed veteran fighters and weapons.

“This is just a simple way of returning the favor to our Syrian brothers that fought with us on the lands of Iraq,” said a veteran of Al Qaeda in Iraq, who said he helped lead the Nusra Front’s efforts in Syria.

The United States, sensing that time may be running out for Syria’s president, Bashar al-Assad, hopes to isolate the group to prevent it from inheriting Syria or fighting on after Mr. Assad’s fall to pursue its goal of an Islamic state.

As the United States pushes the Syrian opposition to organize a viable alternative government, it plans to blacklist the Nusra Front as a terrorist organization, making it illegal for Americans to have financial dealings with the group and most likely prompting similar sanctions from Europe. The hope is to remove one of the biggest obstacles to increasing Western support for the rebellion: the fear that money and arms could flow to a jihadi group that could further destabilize Syria and harm Western interests.

When rebel commanders met Friday in Turkey to form a unified command structure at the behest of the United States and its allies, jihadi groups were not invited.

The Nusra Front’s ally, Al Qaeda in Iraq, is the Sunni insurgent group that killed numerous American troops in Iraq and sowed widespread sectarian strife with suicide bombings against Shiites and other religious and ideological opponents. The Iraqi group played an active role in founding the Nusra Front and provides it with money, expertise and fighters, said Maj. Faisal al-Issawi, an Iraqi security official who tracks jihadi activities in Iraq’s Anbar Province.

But blacklisting the Nusra Front could backfire. It would pit the United States against some of the best fighters in the insurgency that it aims to support. While some Syrian rebels fear the group’s growing power, others work closely with it and admire it — or, at least, its military achievements — and are loath to end their cooperation.

Leaders of the Free Syrian Army, the loose-knit rebel umbrella group that the United States seeks to bolster, expressed exasperation that the United States, which has refused to provide weapons throughout the conflict that has killed more than 40,000 people, is now opposing a group they see as a vital ally.

The Nusra Front “defends civilians in Syria, whereas America didn’t do anything,” said Mosaab Abu Qatada, a rebel spokesman. “They stand by and watch; they look at the blood and the crimes and brag. Then they say that Nusra Front are terrorists."

He added, “America just wants a pretext to intervene in Syrian affairs after the revolution.”

The United States has been reluctant to supply weapons to rebels that could end up in the hands of anti-Western jihadis, as did weapons that Qatar supplied to Libyan rebels with American approval. Critics of the Obama administration’s Syria policy counter that its failure to support the rebels helped create the opening that Islamic militants have seized in Syria.

The Nusra Front’s appeals to Syrian fighters seem to be working.

At a recent meeting in Damascus, Abu Hussein al-Afghani, a veteran of insurgencies in Afghanistan, Iraq and Libya, addressed frustrated young rebels. They lacked money, weapons and training, so they listened attentively.

He told them he was a leader of Al Qaeda in Iraq, now working with a Qaeda branch in Syria, and by joining him, they could make their mark. One fighter recalled his resonant question: “Who is hearing your voice today?”

On Friday, demonstrators in several Syrian cities raised banners with slogans like, “No to American intervention, for we are all Jebhat al-Nusra,” referring to the group’s full name, Ansar al-Jebhat al-Nusra li-Ahl al-Sham, or Supporters of the Front for Victory of the People of Syria. One rebel battalion, the Ahrar, or Free Men, asked on its Facebook page why the United States did not blacklist Mr. Assad’s “terrorist” militias.

Another jihadist faction, the Sahaba Army in the Levant, even congratulated the group on the “great honor” of being deemed terrorists by the United States.