KABUL — Firing rockets and rifles, Taliban militiamen attacked American and Afghan military outposts in a daylong siege on Saturday that killed eight U.S. soldiers and two Afghan security forces in one of the deadliest battles in months, according to U.S. and Afghan officials.

The fighting began early Saturday morning and raged throughout the day in a remote region of eastern Afghanistan in Nuristan province, which borders Pakistan. Staging their attack from steep mountainsides that overlook the outposts in the valley below, on a morning when weather made visibility poor, the Taliban fighters attacked the small American and Afghan bases using rifles, machine guns, grenades and rockets, according to U.S. military officials.

By Sunday morning, when the U.S. military made the attack public in a statement, the area was “largely secure but I do think there is still some activity,” said Capt. Elizabeth Mathias, a U.S. military spokeswoman.

In addition to the eight soldiers killed, several others were injured, said Rear Adml. Gregory J. Smith, but he did not specify the number. The American soldiers called in ground reinforcements, along with attack helicopter, airplanes and surveillance drones during the fighting. U.S. forces eventually repelled the attack while inflicting “a significant amount of casualties” on insurgents, Smith said.

Due to the “very challenging terrain,” the insurgents had “pretty effective firing positions,” Smith said. “It was obviously a very, very difficult day.”

“Virtually everything that could be thrown at it was thrown at it,” Smith said of the American response to the attack.

The U.S. military said it was not immediately clear how many insurgents were involved in the fighting. The attack involved Taliban fighters and appeared to be led by a local commander of the Hezb-e-Islami Gulbuddin insurgent group, which is run by Gulbuddin Hekmatyar, a former mujaheddin leader during the Soviet war in Afghanistan during the 1980s.

The attack took place in a sparsely populated area of forested mountains near the town of Kamdeysh. The deputy police chief of Nuristan province, Mohammad Farouq, said the insurgents intended to seize control of the Kamdeysh area and that hundreds took part in the fighting. He said more than 20 Afghan soldiers and police have gone missing since the fighting began and may have been taken hostage.

“Americans always want to fight in Afghanistan,” said Zabiullah Mujahid, a Taliban spokesman, who took credit for the attack by telephone. “If the Americans want to increase their troops, we will increase our fighters as well.”

He said the battle began about 6 a.m. Saturday and involved 250 Taliban fighters. He claimed that dozens of American and Afghan soldiers were killed, along with seven Taliban fighters. Mujahid also claimed that the district police chief and intelligence chief were among the hostages, but that could not be confirmed.

Farouq, the deputy police chief, said the attack, the biggest his province has seen, was highly organized and began by taking out the police radio system. “Since the attack began I’ve been unable to communicate with the police chief. We are still trying to find out where he is,” Farouq said.

The American soldiers from this outpost were scheduled to depart the area as part of the new U.S. strategy to focus on securing areas with larger populations. Capt. Mathias said the soldiers at the outpost were not expected to leave this month and had not yet begun to prepare for their departure when they came under attack. Smith, who did not specify the number of American soldiers at the outpost, said such isolated bases at times have only “limited impact” against the insurgents.

The provincial governor, Jamaluddin Badar, said that Taliban had regularly attacked American and Afghan government facilities in the Kamdeysh area. The Taliban leadership has appointed a shadow governor in the province, Mullah Dost Muhammad, and has opened a training camp in the forest, he said.

“I have already warned the central government to help us and send more Afghan soldiers, and I warned the American soldiers they need to be more serious and stop the Taliban,” Badar said in a telephone interview. “But unfortunately, nobody listened to me.”

American deaths in Afghanistan have risen sharply this year as Taliban militiamen have gained in strength and numbers and more U.S. forces are involved in operations to combat them, in places such as southern Afghanistan’s Helmand province. American soldiers have had to confront an expanding insurgency in eastern Afghanistan, where fighters can easily slip across the Pakistani border to take refuge.

In a separate incident Saturday, another U.S. serviceman was killed in eastern Afghanistan in a bombing.

The Nuristan province attack — in its severity and location — bore a striking resemblance to a deadly battle in July 2008 in the tiny village of Wanat, in the same region, which left nine U.S. soldiers dead and 27 wounded after several hours of fighting. That battle prompted three investigations and was cited by many as an example of what was wrong with the American military approach to fighting the insurgency. The Wanat attack contributed to the change in strategy to move soldiers from remote areas where they didn’t have the forces to defeat the insurgents and move them to safer, more populated areas.

After the fighting began Saturday, the Afghan military sent a battalion of reinforcements by helicopter to the area, and began searching houses, said Gen. Zahir Azimi, a Defense Ministry spokesman. Afghan officials said at least one policeman and one soldier died in the fighting, and at least one other Afghan soldier was injured.

Badar, the provincial governor, said he was unaware of American plans to abandon their outpost in the area. He said that his province has a shortage of Afghan soldiers and an incompetent police force. The province is at risk of falling to the Taliban if the Americans pull out, he said.

“I request that they stay. If they leave, it will be very dangerous for Nuristan,” he said.

Special correspondent Javed Hamdard contributed to this report.