"I am shocked, as are all Greeks, by this tragic incident," Tsipras said during a visit to the north of the country.
"The Greek government... Will intensify efforts for safety and quality of life at hospitality centres," Tsipras said, referring to the country's camps.
Hours earlier, a 66-year-old Iraqi Kurd and her six-year-old grandson died from the apparent explosion of a cooking gas cannister inside their tent at the camp of Moria.
In an apparent act of rage, migrants then set fire to part of the camp, causing significant damage, police said.
Ensuing clashes between migrants and police left six migrants slightly injured, while several more were taken to Lesbos hospital with lesser burns and respiratory problems.
Some migrants fled the camp after the blast but later returned and calm was restored, a police source said.
Several fires -- not all accidental -- have erupted in refugee camps on the Greek islands, where some 16,000 people became stranded after the European Union signed a deal that was aimed at stemming the influx of migrants.
Part of the camp was badly damaged in a fire on September 19 during clashes between migrants and police, and thousands had to be moved out before returning two days later.
Nearly 66,000 refugees and migrants are currently stranded in Greece, according to official figures.
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