The US armed forces chief says Islamic State (IS) militants are being damaged by air strikes in Syria but air power alone is not enough to defeat them.
Gen Martin Dempsey said a political solution and a ground campaign would both be needed in Iraq and Syria.
Gen Dempsey said that up to 15,000 fighters – to be drawn from Syria’s moderate opposition – would be needed for a ground force in Syria.
On Friday, the UK agreed to join US-led air strikes on IS in Iraq.
French fighter jets are already taking part in strikes in Iraq and Belgium and Denmark are also sending planes.
Speaking at the Pentagon, Gen Dempsey said this week’s strikes in Syria had disrupted IS’s command, control and logistics capabilities.
He said it would take more than air power to recapture lost territory in Syria and neighbouring Iraq but a ground force did not need to involve US troops.
“In fact, ideally for the kind of issues we are confronting there, the only truly effective force that will actually be able to reject Isil (IS) from within its own population is a force comprised of Iraqis and Kurds and moderate Syrian opposition,” he said.
About 40 countries, including several from the Middle East, have joined the US-led coalition against IS.
European countries have so far only agreed to strike targets in Iraq where the government has asked for help.
But US, Saudi and United Arab Emirates aircraft have also attacked IS targets in eastern Syria, including oil installations.
US-led air raids over Syria are now “near continuous”, a US official told AFP news agency on Friday.
US Defence Secretary Chuck Hagel told reporters: “Combined with our ongoing efforts in Iraq, these strikes will continue to deny Isil (IS) freedom of movement and challenge its ability to plan, direct, and sustain its operations.”
On Friday, Russian Foreign Minister Sergei Lavrov questioned the legality of air strikes in Syria because they were carried out without the approval of Russia’s ally, Syrian President Bashar al-Assad.
“It’s very important that such co-operation with Syrian authorities is established, even now that it’s an accomplished fact,” he said on the sidelines of the UN General Assembly in New York.
The Red Cross has also warned that air strikes in Iraq and Syria are adding to an already dire humanitarian situation.
In a statement from its headquarters in Geneva, the group called on all those involved in the conflict to spare the civilian population, and to allow aid agencies to bring relief.
IS controls large parts of north-east Syria and earlier this year seized swathes of northern Iraq including the second city, Mosul.
The Iraqi army, which initially crumbled, is now standing its ground and Kurdish fighters in the north of Iraq are also battling to stem the IS advance.
In Syria, militants are laying siege to the key northern town of Kobane and an estimated 140,000 civilians – mostly Kurds – have fled across the nearby Turkish border.
The situation there remains tense, with Turkish troops trying to prevent Turkish and Syrian Kurds crossing the border to help defend the town.
After a lengthy debate in the UK parliament on Friday, MPs overwhelmingly voted in favour of air strikes, and six RAF Tornados could be called into action over the weekend.
Prime Minister David Cameron told MPs: “This is about psychopathic terrorists that are trying to kill us and we do have to realise that, whether we like it or not, they have already declared war on us.”
Earlier in the week, the UN Security Council adopted a binding resolution compelling states to prevent their nationals from joining jihadists in Iraq and Syria.
The European Union’s anti-terrorism chief says about 3,000 Europeans have gone to join armed Islamist groups in the region.
IS has killed three Western hostages in recent weeks and French public support for the operation surged after the beheading of a French tourist in Algeria by captors who swore allegiance to the group.