The counter-terrorism police chief, General Abdul Manan Farahi, said the remote-controlled devices were found under a bridge on a road leading to the Hazrat Ali Shrine in the west of the capital.
"Thank God we discovered the bombs. They could have caused lots of casualties," he said. "They were huge bombs."
The general, citing intelligence reports, said the Taliban militia had planted the bombs. He said the men behind the attempted attack had been identified but had not been arrested yet.
"We've identified the plotters. We'll get them, they cannot escape," he said.
The Taliban government was overthrown by a US-led invasion in late 2001 for failing to surrender Osama bin Laden after the September 11 attacks on the US.
The Taliban have since been waging an insurgency against the government and tens of thousands of US-led international forces.
An Afghan boy enjoys a ride on a
swing in Kabul on new year's day
Farahi said security was tight across the country with tens of thousands of police and military personnel on alert on the festival day.
Tuesday marks Afghanistan's new year on the solar calendar, and people across the country celebrate by going to shrines and picnic sites with their families.
The new year, known as Norooz, is celebrated in several other countries including Iran, Pakistan and Turkey.
During the 1996-2001 rule of the Taliban, Norooz was banned for being un-Islamic.