The blast occurred before dawn Wednesday more than 1,000 meters (3,200 feet) underground at the Zasyadko mine in Donetsk.
Separatist authorities in Donetsk said in a statement that the blast occurred at a depth of more than 1,000 meters.
Kerry said he hopes the ceasefire will be implemented fully “in the next hours, certainly not more than days.”
Ultra-nationalist organisation Right Sector said that one of its fighters was also killed in the attack.
The deaths of the 3 Ukrainian soldiers came after a two-day lull in clashes with the pro-Russian separatists.
“If no new funds are received from Kiev, then naturally we cannot continue delivering gas to Ukraine,” said Sergei.
One hundred and thirty nine Ukrainian troops and 52 rebels were exchanged
The city lies on the Sea of Azov between mainland Russia and the Russia-annexed Crimean peninsula.
Sources said 4 Ukrainian soldiers had been killed and 21 wounded since the ceasefire came into force.
Ukrainian security services chief Valentyn Nalyvaichenko said one infringement was reported about 50 minutes after the deadline.
The fiercest confrontations focused on the government-held town of Debaltseve, a key transport center.
Clashes appeared only to have increased since a peace agreement was sealed on Thursday.
Putin announces a cease-fire in eastern Ukraine midnight Saturday; says agreement reached on division line for heavy weapons’ pullback.
German chancellor meets Canadian PM to discuss a solution to the ongoing violence in Ukraine.
Explosion outside separatist stronghold rocks Ukraine, no casualties or damage were immediately reported.