The preliminary investigation found one of the Afghan security guards protecting the DHL compound opened fire on the car carrying the two foreigners when it pulled into the company headquarters, said Mirza Mohammad Yarmal, an Interior Ministry official.
The guard then put the Kalishnikov rifle to his own head and killed himself, Yarmal said. Blood was on the vehicle's windshield and pooled on the ground in front of DHL headquarters.
Yarmal said the guard had been hired about a month ago from a Pashtun area just north of Kabul. The Taliban draws many of its fighters from the Pashtun ethnic group, but police had no conclusive evidence linking him to the insurgents.
A Taliban spokesman denied involvement in the attack.
DHL's headquarters are in a relatively secure part of in downtown Kabul, across the street from the Iranian Embassy and close to Afghanistan's intelligence service.
Gerold Beck, a DHL spokesman at its headquarters in Bonn, Germany, would only say the company was working with authorities to "clarify the situation."
Police arrested 13 people after the incident, including DHL guards and employees, said Zemeri Bashary, the Interior Ministry spokesman.
The attack follows the slaying in Kabul of a dual South African-British citizen aid worker - Gayle Williams, 34 - by gunmen earlier in the week. The Taliban immediately claimed responsibility for that shooting, saying the woman had been proselytizing.
Williams worked with the group Serving Emergency Relief and Vocational Enterprises to help disabled Afghans. Her mother and sister appeared at a news conference in Kabul Saturday ahead of the funeral planned for Sunday.
"If Gayle could talk with us now, her view would not have changed," her sister, Karen Williams said. "Her faith in the Afghan people would remain the same. I know Gayle would forgive those responsible for this act and would tell us not to hold a grudge against them. We also forgive them, just as Gayle would have done."
Security has deteriorated around Afghanistan in the last two years, although violence against Westerners in the capital has been relatively rare until recently. Security in Kabul has soured dramatically following a rash of kidnappings and security warnings.
International security companies warned clients Saturday about intelligence indicating militants were targeting restaurants frequented by Westerners for a large-scale attack.
Meanwhile, Turkey's foreign minister confirmed three Turkish nationals working on a communications project were kidnapped in the eastern province of Khost Thursday.
Speaking at a joint news conference in Kabul with visiting Turkish Foreign Minister Ali Babacan, Afghan Foreign Minister Rangin Dadfar Spanta said officials believe the three were abducted by a criminal gang.
In the southern province of Ghazni, governor's spokesman Ismail Jahangir said two aid workers from Bangladesh had been kidnapped on Thursday.