"We want to build two closed centres in (the northern region of) Serres and the greater Athens area with 1,000 places," migration minister Notis Mitarachi told Skai TV.
"We need the backing of local communities. We cannot leave all (these) people on the islands," he said.
Mitarachi said the camps would host asylum seekers who arrived after March 1, when Turkey announced it would no longer prevent people from trying to cross into the European Union.
Residents of a town in the Serrres region rumoured to host one of the camps staged protests earlier this week and local officials declared their opposition to the plan.
Over 1,700 migrants have landed on Lesbos and four other Aegean islands from Turkey over the past week, adding to the 38,000 already crammed into abysmal and overstretched refugee centres.
Mitarachi on Saturday also said state support for refugees would be limited, and that they would be asked to leave camps after securing protected status.
"Accomodation and benefits for those granted asylum will be interrupted within a month. From then on, they will have to work for a living. This makes our country a less attractive destination for migration flows," the minister said.
The new surge has ramped up already high tensions on Lesbos, an island that has been on the migration frontline for years.
Frustration exploded into violence last weekend with mobs setting up roadblocks, attacking cars carrying NGO workers and beating journalists.
Far-right militants from other parts of Europe have travelled to Lesbos and the Greek border with Turkey, among them Swedish far-right leader Jimmie Akesson, who reportedly handed out flyers at Edirne with the message "Sweden is full".
On Friday, two Germans and two Austrians - identified as hardline nationalists by local media - told police they had been attacked and beaten on the central Lesbos market.
One of the four, who claimed they were journalists, was identified as Mario Mueller, a German member of the far-right Identitarian Movement.
On Saturday, anti-fascist activists organised a gathering in support of refugees on Lesbos.
"We need to react in some way because we've reached a point where fear is taking hold," said Maria Psomadaki, a retired teacher.
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