"Non-resident investors who held deposits prior" to the bailout and lost "at least 3 million euros will be eligible to apply for Cypriot citizenship," he told a Russian business conference in the coastal resort of Limassol.
"We believe that a number of measures to be adopted could on the one hand mitigate to some extent the damage the Russian business community has endured," Anastasiades said.
He said the measures, primarily affecting Russians, would be approved at a two-day cabinet meeting starting on Monday.
"These decisions will be deployed in a fast-track manner and other measures, currently under consideration," said the president, whose country sealed an EU bailout last month to rescue it from bankruptcy.
Most of the money being raised by Cyprus to qualify for the bailout is to come from a hit of as much as 60 percent on more on deposits above 100,000 euros at the Mediterranean country's two largest banks.
Russians have billions of euros in deposits parked in Cyprus, with estimates ranging from 5-31 billion euros. Moscow was angered when it emerged they would lose part of their money under "haircuts" demanded in return for an EU bailout.
The government is also "examining various scenarios which could permit the compensation of part of the losses which shareholders of banks, holders of debt securities and depositors have suffered," Anastasiades said.