Turner called his father in suburban Kansas City after the attack, 82-year-old Lionel Turner told The Associated Press.
"He said he was burned a little, but that he wasn't hurt," the father said. "He's got more guts than a Missouri mule."
It was not possible to reach others who had been staying at the guest house to verify Turner's account. UN staff were evacuated to Dubai for counseling, the UN said. Turner did not have a weapon when he spoke with an AP reporter.
About a mile away from the guest house, one rocket struck the "outer limit" of the presidential palace but caused no casualties, presidential spokesman Humayun Hamidzada said. Two more rockets slammed into the grounds of the expensive Serena Hotel, favored by many foreigners.
President Hamid Karzai condemned the attacks as "an inhuman act" and called on the army and police to strengthen security around all international institutions.
Taliban spokesman Zabiullah Mujahid claimed responsibility in a telephone call to the AP, saying three militants with suicide vests, grenades and machine guns carried out the guest house assault. The Interior Ministry said there were three attackers and all were killed.
The attack followed a warning last week by the Taliban, which threatened anyone working on the runoff election between Karzai and former Foreign Minister Abdullah Abdullah.
"This is our first attack," Mujahid said.
UN spokesman Adrian Edwards said five UN staff were killed and nine other UN employees were wounded.
Afghan police and UN officials said 11 people in all were killed, including the UN staff, three attackers, two security guards and an Afghan civilian.
The dead included the brother-in-law of one of Afghanistan's most powerful governors, Gul Agha Sherzai. The man was killed by a stray bullet as he watched the gunfight from a nearby house, according to provincial spokesman Ahmad Zia Abdulzai.
Edwards said the UN would have to evaluate "what this means for our work in Afghanistan."
"This has clearly been a very serious incident for us," Edwards said. "We've not had an incident like this in the past. ... We obviously will have to adjust our security in light of this."
An internal UN memo ordered restrictions on movement for the rest of the week and said UN departments would be reviewing its list of critical and nonessential personnel, suggesting some people may be moved out of the country for their own safety.
The August 19, 2003, truck bombing of the UN headquarters in Baghdad, which killed 22 people, prompted the UN to pull out of Iraq for several years.
Afghans are to vote in a second-round election after UN-backed auditors threw out nearly a third of Karzai's votes from the August 20 ballot, determining widespread fraud. That pushed Karzai's totals below the 50 percent threshold needed for a first-round victory in the 36-candidate field.
Dozens of people were killed in Taliban attacks during the August balloting, helping drive down turnout.