...blast at an army depot killed at least three people on Friday.
Kasicky offered his resignation after the explosion near the western Slovak town of Novaky, in which dozens were also injured.
Army spokesman Vladimir Gemela said rescue teams were still searching on Monday for five people who went missing after the explosion, which occurred at an army facility used to deactivate ammunition such as mines and missiles.
"I respect the work of Minister Kasicky, and I will not propose his dismissal," Fico told the all-news TV channel TA3.
According to law, the prime minister proposes any dismissal of ministers to President Ivan Gasparovic. Ministers can also submit resignations directly to president.
Gasparovic's spokesman was not immediately available for comment. TA3 said the president had not yet received any official notification from Kasicky of his offer to resign.
Test Renault Austral: Fakt chcete opět škodovku?
Denně v pohotovosti: 10 nejznámějších poválečných československých autobusů
Sen o levném cestování elektromobily se rozplývá. V Evropě je návrh, podle kterého se elektromobilům zdaní každý ujetý kilometr
Electra dorazila do Česka a tentokrát to není ta Baťova. Hlavní roli hrají elektromobily
Svatý grál ctitelů supersportů: Lamborghini Miura slaví 60 let
