Mr Saleh shows a photo of one of the alleged attackers
The Afghan authorities say they have arrested one of a group of Taleban attackers who stormed the luxury Serena hotel in Kabul on Monday evening.
It is thought at least eight people were killed in the bomb blasts and gunfire, two of them attackers as well as a number of hotel guards and guests.
Guests, including the Norwegian foreign minister, were taken to the hotel cellar for safety during the attack.
The Serena is the main Kabul hotel for foreign visitors.
Monday's attack was the latest in a string of Taleban attacks in the capital in recent weeks.
'Changed his mind'
There are still conflicting accounts of how the attack unfolded and the numbers of dead.
Afghan intelligence chief Amrullah Saleh told journalists on Tuesday that three Taleban, all wearing suicide jackets, stormed the heavily protected hotel.
He said one was shot by a hotel guard outside the building, causing his jacket to explode. Another, Mr Saleh said, died after he detonated his jacket inside the building.
The third attacker, Mr Saleh said, was arrested shortly after the attack began.
"The third person, after killing a number of the guests, maybe he changed his mind for some reason, he didn't detonate himself," Mr Saleh said, the Associated Press news agency reports.
"He changed his clothes and later when security forces searched the premises, he was arrested."
Mr Saleh also said that a man who drove the attackers to the hotel had been arrested, as well as two men who had given them accommodation in Kabul.
Another man - said to have provided the weapons and explosives - was arrested in the eastern city of Jalalabad.
Shortly after news of the attack broke, a Taleban spokesman said four of their fighters, all wearing explosive jackets, were involved.
The dead include a Norwegian journalist, Carsten Thomassen, 39, who worked for the Oslo newspaper, Dagbladet, and at least one US citizen.
A Filipina spa supervisor at the hotel was injured in the attack and later died.
A policeman guarding the Serena after the attack
It is still not clear if more guests were killed. The precise number of hotel staff casualties also remains confused.
Norwegian Foreign Minister Jonas Gah Store was among guests who took refuge in a cellar.
Norwegian foreign ministry spokeswoman Anne Lene Dale Sandsten told the BBC News website Norwegian officials had been in a meeting one level down from the reception when they heard shooting and "then a big blast go off one level up".
"We had security people with us and we were told to lie down."
Suzanne Griffin, a US aid worker who had been in the hotel gym, told the Associated Press news agency the gunfire had been "close enough that plaster came off the ceiling".
"We had to step over a woman's dead body - she was one of the gym people," she added.
Security in much of Afghanistan has deteriorated in the past two years as the Taleban and their allies have renewed attacks on Afghan security forces and Western troops.
The worst of the violence has been in the south and east of the country.
In December the Taleban carried out two suicide bombings in Kabul, killing 13 people in one attack.
Later that month, a rocket attack near the Kabul governor's residence killed five people.
US-led forces toppled the Taleban government in late 2001.