Barack Obama met with Afghan President Hamid Karzai on Sunday, telling him the U.S. will fight terrorism "with vigour" if elected, according to an Afghan official.

Obama also continued to press for a troop "surge" to help battle the increasingly deadly situation in Afghanistan.

"I believe U.S. troop levels need to increase," the presumptive Democratic nominee said. "And for at least a year now I have called for two additional brigades. Perhaps three."

That's about 7,000 or more new U.S. troops Obama says he would bring to Afghanistan as president.

Obama has criticized Karzai in the past for not doing enough to improve the security and political situation in war-torn Afghanistan. Obama and Karzai did not say what they discussed during their two hour meeting at the presidential palace in Kabul, but officials from both sides say the discussion were fruitful.

U.S. embassy spokesperson Mark Stroh told reporters talks included the economy, corruption, and Afghanistan's security situation. An official with Karzai's office said Obama offered a positive message.

"Sen. Obama conveyed ... that he is committed to supporting Afghanistan and to continue the war against terrorism with vigour," said Humayun Hamidzada, Karzai's spokesman.

Karzai's staff also released a video of the meeting. It showed the two men seated and chatting by a fireplace. Both were smiling.

Before meeting Karzai, Obama visited U.S. troops at Camp Eggers, where he praised their efforts.

"To see young people like this who are doing such excellent work, with so much dedication ... it makes you feel good about the country," Obama said.

He landed in Afghanistan Saturday for an unannounced trip. The country is a key part of his anti-terrorism strategy. Obama has said he wants to pull U.S. troops out of Iraq and instead focus anti-terrorism efforts on Afghanistan.

Obama, along with others in the delegation, held a briefing Saturday with the provincial governor of Nangarhar, Gul Agha Sherzai, a former warlord.

"Obama promised us that if he becomes a president in the future, he will support and help Afghanistan not only in its security sector but also in reconstruction, development and economic sector," Sherzai told The Associated Press.

Security was extremely tight for the visit and media access to Obama was limited. His itinerary in the war zones was a closely-guarded secret.

"He didn't bring any reporters with him on the plane and that's very rare," CNN's Reza Sayah told Â鶹´«Ã½net on Sunday morning.

Obama is also expected to visit Europe, Iraq and Israel during his tour. Analysts say the international trip is part of an effort by the Obama camp to boost his foreign policy credentials. His Republican rival, John McCain, has questioned Obama's readiness to lead the U.S. on the world stage.

"Obama could not have taken on Sen. John McCain without having visted Afghanistan," said Sayah.

With files from The Associated Press