Obama also warned Europe's leaders and students at a meeting that, for geographical reasons, Europe faced a bigger threat than the US from al-Qaeda.
No troop promises
Both Angela Merkel, the German chancellor, and Nicolas Sarkozy, the French president, met with Obama before the summit got under way.
But despite warm support they gave no indication that they will send more soldiers to Afghanistan.
Speaking at a news conference with Obama on Friday, Sarkozy gave his support to "the new American strategy in Afghanistan" but added there would be "no strengthening of French troops" in the country.
He said France, which has just been admitted back into Nato's military command structure after a 43-year absence, was ready to do more in the field of police training and economic aid.
Rob Reynolds, Al Jazeera's correspondent reporting from Strasbourg, said it appeared Sarkozy and Obama "have agreed not to disagree over this".
"It does look as if the American side here is not going to push the issue ... because they recognise the political realities - it is simply not going to happen," he said.
"America's stature has been very materially diminished by the global economic crisis alone," he said.
Despite Sarkozy's unwillingness to commit more troops, Obama said he was "grateful" for Washington's relationship with France.
"France has already been a stalwart ally when it comes to Afghanistan," he said.
Hillary Mann Leverett, a former diplomat and Afghanistan director at the US National Security Council, told Al Jazeera that European leaders are unlikely to pledge troops to Afghanistan for a policy they are unsure about.
"[European nations] are happy to put money up for something they can claim credit for, for example, to train police... but to train the Afghan military, you don't get credit for that."
"Obama needs to dial back expectations that the Europeans and Nato is the answer for Afghanistan. He should look more to regional players."
In another move, Sarkozy said he will accept one Guantanamo Bay detainee, an Algerian, to be settled in France.
The acceptance of the detainee marks a possible breakthrough in Obama's attempt to close the prison camp and resettle dozens of prisoners in foreign lands.
Share Afghanistan burden
Merkel, the summit's co-host, also stressed Germany's commitment to shouldering its share of the burden in Afghanistan after talks with Obama in Baden Baden in Germany, but she also refused to send more troops to Afghanistan.
"We have a great responsibility here. We want to carry our share of the responsibility - militarily, in the area of civil reconstruction and in police training," Merkel said.
"[The Obama administration's approach to Afghanistan] complements
fully what Germany has in mind, a comprehensive approach,'' she said.
Britain said it would consider dispatching extra forces to help out during Afghanistan's presidential election scheduled for August.
European nations have been reluctant to commit extra troops to Afghanistan in support of about 70,000 mostly Nato soldiers stationed there.
Hamish Macdonald, Al Jazeera's correspondent, said from Strasbourg: "The United States has already said that it will deploy another 17,000 troops to the country, which was followed up by an announcement that another 4,000 US troops will be going there to train Afghan security forces."
Hillary Clinton, the US secretary of state, said on Friday that Obama will not push Nato members on the numbers of troops they can deploy, saying: "The Nato summit is not a pledging conference."