The phone call between Obama and Karzai on Saturday is the first reported contact between the two leaders and comes more than two weeks after the Nov. 4 U.S. election.
The United States has some 32,000 American forces in Afghanistan, a number that will be increased by thousands next year.
Fighting terrorism and the insurgency "in Afghanistan, the region and the world is a top priority," Karzai's office quoted Obama as saying during the conversation.
Afghanistan has long pressed the U.S. to tackle what it calls the bases of terrorism in Pakistan, and Obama's reported pledge will likely please Karzai, who has accused Pakistan's intelligence service of supporting the Taliban in plotting bombings and other attacks in Afghanistan - claims that Pakistan, a key U.S. ally in its war on terror, flatly denies.
Obama in the past has expressed frustration with Pakistan's efforts to go after militants in its territory. During the presidential campaign he said that, "If Pakistan cannot or will not act, we will take out high-level terrorist targets like (Osama) bin Laden if we have them in our sights."
Cross-border U.S. missile strikes as well as ground operations by U.S. forces along the border have increased significantly in recent months.
Last week U.S. troops launched a barrage of artillery at insurgents attacking their position from inside Pakistan's volatile tribal region, and since mid-August, the United States is suspected of launching at least 20 missiles from unmanned drones based in Afghanistan, killing scores of suspected extremists and angering the Pakistani government.
Over the past month, NATO and Pakistani forces have been cooperating in so-called Operation Lion Heart - a series of complementary operations that involve the Pakistani military and Frontier Corps, and NATO on the Afghan side.
The top spokesman for the NATO-led force in Afghanistan, Brig. Gen. Richard Blanchette, said Sunday that cooperation between Afghan, NATO and Pakistani troops is "the best it has ever been."
"You finally have those who are really conducting the operations, the soldiers who know exactly where on the other side the operations are happening, so you can have a movement which you could compare to the movement of a hammer and an anvil," Blanchette said.
In the phone call, Obama pledged to increase U.S. assistance to Afghanistan, according to a statement from Karzai's office. An aide to Karzai said the increase would include economic and military assistance.
It was not clear why it took more than two weeks for Obama to speak with Karzai. Obama spoke with at least 15 world leaders in the first three days after his election.
Obama has chided Karzai and his government in the past, saying it had "not gotten out of the bunker" and helped to organize the country or its political and security institutions.
In the latest violence, U.S. and Afghan troops killed 17 militants in the Shah Wali Kot district of Kandahar province on Saturday, the U.S. military said. A statement Sunday said that helicopters carried the troops into "a known insurgent safe haven" to attack "enemy supplies and personnel."
Elsewhere in Kandahar province, Afghan and coalition troops killed 11 militants traveling in two vehicles on Saturday, provincial police Chief Matiullah Khan said.
In neighboring Helmand province, NATO-led troops killed a senior Taliban commander, Mullah Assad, on Wednesday, a NATO statement said Sunday. Assad was linked to attacks in Helmand's Garmser district, an area of southern Afghanistan rife with insurgent activity.
The U.S. also said it killed two militants and a female civilian in Zabul province on Thursday, according to a statement Sunday. It did not provide details on how the civilian was killed.