A Western-brokered ceasefire agreed in February has been punctuated by frequent deadly incidents.
In a fresh bid to restore peace, Ukrainian government and separatist representatives last week agreed to seek to end ceasefire violations from Tuesday as children began school term.
But after several days of a relative lull in the war-ravaged industrial east, a group of civilians and law enforcement officials were caught in an ambush in the rebel-controlled Lugansk region during an anti-smuggling operation.
"During a clash, a volunteer and a member of the state fiscal service were killed," Lysenko told reporters, saying that it was an ambush and that the road was mined.
"An enemy sharpshooter was also at work," he added.
In July, Ukraine set up groups of law enforcement officers, tax officials and volunteers to combat smuggling of contraband goods across the demarcation line in eastern Ukraine.
The two victims were the first participants in such a group to be killed.
An aide to President Petro Poroshenko, Yuri Biryukov, wrote on his Facebook page that a member of the SBU security service and several paratroopers were wounded as a result of the attack.
The attack came as EU sources said the 28-nation bloc would extend sanctions for another six months against Ukrainian and Russian figures accused of backing pro-Moscow rebels.
"There is a political agreement; (officials) agreed to extend the sanctions for six months to March next year," one source told AFP after a meeting of diplomats from European Union Nations to discuss the sanctions.
The sources said EU member states are expected to formally endorse the decision ahead of the scheduled expiry of the sanctions on September 15.
But some ordinary Ukrainians said they were sceptical that the ceasefire would last long.
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