The half kilo of industrial explosive was found in the capital Bratislava on Thursday, next to a second container full of the Yugoslav explosive, Pentrix.
Detonators needed to ignite the compounds were also found in the bags, police said.
"The bags were found under a trash box," Interior Ministry spokesman Boris Azaltovic told journalists, declining to speculate on a motive or who was responsible.
"Police patrols searched the street yesterday...and again today...after receiving information from the Slovak Information Service (the Slovak secret service)."
NATO Secretary-General Jaap de Hoop and Muhammad al-Baradei, director general of the International Atomic Energy Agency (IAEA) are to address the meeting on 1 June.
Though it has had no previous incidents involving guerrilla groups, Slovakia has been a strong supporter of the US-led war in Iraq and currently has 105 troops there.
Experts said the amount of the explosives was not big enough to bring a building down, but could cause extensive damage to the immediate area where they detonate, including loss of life.
Police said an investigation was under way but no arrests have been made.
The possible attack comes at a time when General Jaap de Hoop Scheffer plans to overhaul the organisation's strategies and financing.
NATO members will also be asked to transform their armed forces - many of which are still designed for Cold War strategies.