If true, the confessions would be a possible breakthrough in a case that chilled foreigners with its echoes of Iraq.
The men have "confessed to their crime and have told us how they designed this plan", Interior Minister Ali Ahmad Jalali said on Thursday in Kabul.
He said the six were also suspected of armed robbery.
The three UN election workers - one each from the Philippines, Northern Ireland and Kosovo - were seized at gunpoint last October and shown looking pale and scared in a video shot by their abductors.
They were released unharmed a month later, but the incident piled pressure on the roughly 3000 foreign civilians living in the Afghan capital, for whom much of Afghanistan is already off-limits for fear of Taliban-led rebels.
A Taliban splinter group claimed responsibility for the kidnapping, though officials and diplomats have suggested that criminals - possibly working for factions that oppose the growing authority of the US-backed government - were responsible.
The UN was "very pleased" at the break and hoped the case could be concluded as soon as possible so that the suspects can go on trial, spokeswoman Ariane Quentier told The Associated Press.
She declined to comment on what the abductors' motive might have been.
Karzai's government is hard put
to protect foreign aid workers
Jalali declined to identify the six, but law-enforcement officials previously said one was Tilagai, a suspected robber detained after a shootout with police north of Kabul last month. Many Afghans use only one name.
Officials have said another man detained in April was suspected in both the kidnapping and the slaying of a British development worker in Kabul on 7 March, though it was unclear on Thursday if he remained in custody.
It also was unclear whether any of the six in police custody were suspected of seizing an American civilian in Kabul last month. The man escaped by throwing himself from a moving car.
Such incidents have revived concern that Afghan criminals and insurgents may copy the tactics of their counterparts in Iraq, where more than 150 foreigners have been abducted and many killed.
Security officials warned aid workers in Kabul earlier this week that criminals might try to kidnap another foreigner in an attempt to force Tilagai's release.
Jalali made no mention of such a threat, but said police had set up extra road blocks in the city and the nearby Paghman valley, which security forces combed in November in search of the kidnappers' hideout.