Cases have surged in Ukraine in recent days, with the total now reaching more than 29,000, according to official figures. 

Since Friday, the number of cases has risen by over 3,600, 21 percent more than in the previous seven days.

"Today we have very alarming figures," Health Minister Maksym Stepanov wrote on Facebook, saying the tally for the last 24 hours was the highest since the outbreak hit. 

Some experts said the uptick was due to an increase in testing rather than a second wave of the disease. 

But Stepanov berated Ukrainians for failing to stick to safety rules after lockdown restrictions were eased last month with the reopening of outdoor cafes, beauty salons, dental clinics and parks.

He promised to come up with some "urgent" steps to slow down the spread of the virus.

"The threat is still here, but take a look at the streets, take a look at what is happening around you," he said.

"We all came out of isolation, we all decided that (the virus) no longer exists," he added.

Lockdown measures are set to further ease this month with a resumption of public transport, including metro systems and long-distance and local train services.

Ukraine launched domestic flights on June 5 and will restart international flights on Monday.

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