Yiannis Mouzalas told To Vima radio that boats taking refugees to the Greek mainland would soon be using a second port to ease pressure on the island of 85,000 inhabitants.
"Mytilene currently has 15,000-17,000 refugees and this is the official figure from all services," Mouzalas, a junior interior minister, told the station.
"We are placing emphasis here because the situation is on the verge of explosion," he said.
Lesbos is one of several Greek islands struggling with an influx of thousands of migrants, many of them Syrian refugees, setting sail from the nearby Turkish coast.
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"We hope that in the next five days the (islanders) and the refugees will see clear signs of improvement," Mouzalas said.
Lesbos mayor Spyros Galinos on Saturday had called on the island residents to boycott national elections on September 20 in protest at the refugee buildup.
"We call on the people of Lesbos not to take part in the upcoming elections and we state our intention not to place ballots unless immediate measures are taken to deescalate the situation," Galinos said in a statement.
Police reinforcements were sent today to the island after Syrian refugees were targeted with Molotov cocktails.
Two 17-year-old boys were arrested after throwing two Molotov cocktails at refugees sleeping in a park, injuring a Syrian man in the process.
Syrians have been granted priority in the registration process, sparking tensions with other migrants forced into long waits on the island.
More than 230,000 people have landed on Greek shores this year, with the numbers soaring in recent weeks as people seek to take advantage of the calm summer weather.