US-led air strikes have disrupted Islamic State (IS) militants but the fight against them will take years, a Pentagon spokesman has told the BBC.
The comments came as activists reported new strikes around the town of Kobane, near Syria's border with Turkey.
Kobane has been besieged by IS fighters for several days, forcing about 130,000 Syrian Kurds to flee into Turkey.
IS has seized large areas of Syria and Iraq, and the US has launched nearly 200 air strikes in Iraq since August.
However, Monday's strikes 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, which hit multiple targets in the north and east of Syria.
'Exodus from Raqqa'
Speaking in Washington, Rear Adm John Kirby said the air strikes in Syria had successfully degraded IS 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 IS 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."
He said the threat had engulfed Libya, Lebanon, Syria, Iraq and Yemen and had "distorted the image of Islam and Muslims."
Meanwhile, the BBC understands that the UK Parliament will be recalled on Friday to discuss Britain's possible role in air strikes on IS targets.
Speaking on Monday, UK Prime Minister David Cameron said an international coalition was needed to "destroy" IS, adding that it was a fight "you cannot opt out of".
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.
President Obama said al-Qaeda-linked militants, known as the Khorasan Group, were also targeted by air strikes in Syria.
US officials say the group had been plotting "imminent attacks" against the West, and had established a safe haven west of Aleppo.
Syrian President Bashar al-Assad, quoted by state media, said he supported any international efforts to combat "terrorism" in Syria.
However, Iranian President Hassan Rouhani, a Syrian government ally, said military action in Syria lacked "legal standing" without a UN mandate or approval from the Syrian government.
- Formed out of al-Qaeda in Iraq (AQI) in 2013, IS first captured Raqqa in eastern Syria
- It captured broad swathes of Iraq in June, including Mosul, and declared a "caliphate" in areas it controls in Syria and Iraq
- Pursuing an extreme form of Sunni Islam, IS has persecuted non-Muslims such as Yazidis and Christians, as well as Shia Muslims, whom it regards as heretics
- Known for its brutal tactics, including beheadings of soldiers, Western journalists and aid workers
- The CIA says the group could have as many as 31,000 fighters in Iraq and Syria
- The US has been launching air strikes on IS targets in north-eastern Iraq since mid-August