The fight against jihadist group Islamic State (IS) will take years, a US military spokesman has told the BBC.
Rear Admiral John Kirby also said that US-led air strikes against IS in Syria had disrupted the group's capabilities.
The remark came as President Barack Obama thanked Arab states for help and Secretary of State John Kerry said more than 50 nations had agreed to fight IS.
IS has seized large areas of Syria and Iraq, and the US has launched nearly 200 air strikes in Iraq since August.
Monday's strikes however expanded the anti-IS campaign across the border into Syria for the first time.
Activists say at least 70 IS militants, 50 other al-Qaeda-linked fighters and eight civilians were killed in the strikes.
Speaking in Washington, Rear Adm John Kirby said the air strikes in Syria had successfully degraded IS's capabilities.
"We think we have hit what we were aiming at," he said.
However, IS was good at adapting and reacting to changes, he said, adding that the group presented a "serious threat" that would not be eliminated "within days or months."
"It's going to take a serious effort by all involved. We do believe that we're talking about years here."
The strikes targeted the IS main headquarters in its stronghold of Raqqa, north-eastern Syria, as well as training compounds, vehicles and storage facilities in several other areas.
Residents in Raqqa have told journalists that the air strikes have had a big impact on IS fighters.
One activist in Raqqa, Abu Yusef, told AFP news agency that the militants were "focused on trying to save themselves now".
Abo Mohammed, a local resident, told Reuters that the city's main administrative building had been hit by four rockets, and hundreds of fighters who had been controlling traffic and security in the street had now gone.
Residents were also "fleeing towards the countryside" to avoid the strikes, he said. "There is an exodus out of Raqqa as we speak."
Meanwhile, Mr Kerry told reporters that more than 50 countries had agreed to join efforts to fight IS.
"We will not allow these terrorists to find a safe haven anywhere," he said.
On Tuesday, Mr Obama hailed the support of Arab nations in the air strikes, saying: "This is not America's fight alone."
Saudi Arabia, the United Arab Emirates, Jordan, Bahrain and Qatar had taken part in or supported the strikes in Syria, Mr Obama said.
Speaking in New York, Saudi Foreign Minister Prince Saud al-Faisal said: "Today we are facing a very dangerous situation as terrorism has turned from cells into armies.
"It has formed a dangerous cordon engulfing Libya, Lebanon, Syria, Iraq and Yemen."
"This terrorism has distorted the image of Islam and Muslims," he added, in quotes carried by the Saudi Press Agency.
The Pentagon said warplanes, drones and Tomahawk cruise missiles were used in Monday's air strikes.
They were organised in three separate waves with US fighter jets carrying out the first set, and Arab nations participating in the second and third, US military officials said.
US state department spokeswoman Jan Psaki said the US had warned Syria in advance "not to engage US aircraft".
But she added that Washington had not requested permission or given advance notice of the timing of the attacks.
(BBC)