The paper said that Sergei Bagapsh made the statement at the meeting with the vice-president of the non-governmental International Crisis Group, Alain Delatroz, and the director of the organization's office for the Caucasus region, Lawrence Sheets.
"We are building an independent, legal and democratic state and are not planning to backtrack from this path," Bagapsh said.
"We have no illusions that tomorrow the whole world will recognize us, but it is important for us that the world's largest country, Russia, has recognized us," he added.
Russia recognized Abkhazia and South Ossetia, another former Georgian republic, as independent states two weeks after the end of a five-day war with Georgia last August. Fighting began when Georgian forces attacked South Ossetia in a bid to bring it back under central control.
Bagapsh also said Abkhazia was ready for cooperation with any country wishing "to establish normal relations." However, he also said that Abkhazia would not hold talks "with the Saakashvili regime."
Nicaragua is the only to country to have joined Russia in recognizing the two republics.