Updated at 9:25 a.m. ET
(CBS/AP) KABUL, Afghanistan - A militant arrested in the attacks on the Afghan capital and three other cities has confessed that the 18-hour assault was carried out by the Haqqani network, a lethal group of fighters with ties to the Taliban and al Qaeda, a top Afghan security official said Monday.
Thirty-six insurgents were killed during the brazen attacks that also claimed the lives of eight policemen and three civilians, said Interior Minister Besmillah Mohammadi.
Though the death toll was much lower than in other attacks, the dramatic assault on multiple targets showed that militants are far from beaten and can still penetrate Afghan security even in the heart of the capital after 10 years of war. The attacks in Kabul, Nangarhar, Paktia and Logar provinces also underscored the security challenge facing government forces as U.S. and NATO troops draw down and prepare to leave by the end of 2014.
Preventing further attacks is a serious challenge for the Afghan authorities, especially trying to keep weapons from coming into Kabul, and they've asked for scanning equipment to help do it, CBS News correspondent Allen Pizzey reports from the Afghan capital.
President Hamid Karzai said Monday the attacks were an "intelligence failure by us and especially NATO" that allowed the militants to enter Kabul and other targeted cities, and called for a full investigation. Karzai, however, praised the Afghan security forces' response to the attacks.
It was the most widespread assault in the Afghan capital since an attack on the U.S. Embassy and NATO headquarters last September also blamed on the Haqqani network, which commands the loyalties of an estimated 10,000 fighters considered one of the most serious threats to NATO in Afghanistan.
"One terrorist who was arrested in Nangarhar province confessed, saying 'It was the Haqqani network that launched these attacks,"' Mohammadi told reporters in Kabul.
Afghan and U.S. officials are trying to coax the Taliban who are not as closely linked with al Qaeda as the Haqqanis to negotiate a political resolution to the war. If the Haqqani faction of the insurgency is behind the recent attacks, it could be easier to sell the idea of making peace with the Taliban to skeptics who say it amounts to making a deal with the enemy.
The Haqqanis, led by Jalaluddin Haqqani and his son Sirajuddin, operate primarily in provinces along Afghanistan's eastern border with Pakistan. NATO spokesman Carsten Jacobson once described the group as a "family clan, a criminal patronage network and a terrorist organization."
Former Joint Chiefs of Staff Chairman Adm. Mike Mullen said in October 2011 the Haqqanis act as a "veritable arm" of the Pakistani intelligence agency an accusation Islamabad denied. Mullen accused the network of staging the Sept. 13 attack on the U.S. Embassy and NATO headquarters, as well as a truck bombing that wounded 77 American soldiers in Wardak province.
Taliban spokesman Zabiullah Mujahid said the attacks had been planned for two months to show the insurgency's potency after NATO officials called the Taliban weak. He told The Associated Press on Monday that they did not mark the start of the insurgents' spring offensive, which would begin shortly.
"It is a message for the spring offensive but it has not yet started," Mujahid said.
U.S. Ambassador Ryan Crocker said Sunday's attacks showed why the U.S. should not try to hasten the exit from Afghanistan.
"To get out before the Afghans have a full grip on security, which is a couple years out, would be to invite the Taliban, Haqqani and al Qaeda back in and set the stage for another 9/11," Crocker said.
The attacks on the Afghan capital ended Monday morning when insurgents who were holed up overnight in two buildings were overcome by heavy gunfire from Afghan-led forces and pre-dawn air assaults from U.S.-led coalition helicopters.
CBS News' Fernando Suarez reports that new explosions at around 1:30 a.m. signaled the launching of a night attack by security forces to smoke out the final insurgents. Blasts and helicopter patrols of the area lasted until 6:30 a.m. when it suddenly stopped.
Rocket-propelled grenades were fired one after another into a building in the center of the city, from where the insurgents launched one of their attacks on Sunday. The building, which is under construction, overlooks the presidential palace, Western embassies and government ministries. The U.S., German and British embassies and some coalition and Afghan government buildings took direct and indirect fire, according to Lt. Col. Jimmie Cummings, a spokesman for the U.S.-led coalition.
"A Haqqani connection is a possibility, but still too early to determine for sure," said Cummings, the NATO spokesman. "We will look strongly at that."
Shortly before 3 a.m., coalition helicopters began flying over the structure. At 4:23 a.m. a religious cleric began calling Muslim worshippers to prayer over a loudspeaker in the area. During the next 15 minutes, troops launched five rocket-propelled grenades into the building. More followed.