Bagapsh, who died after lung surgery, "was a staunch supporter of friendship and alliance with Russia," Russian President Dmitry Medvedev said in a statement.
"He worked tirelessly on strengthening the deep ties between our countries."
In power since 2005, Bagapsh, 62, was re-elected head of the separatist region by a crushing margin in 2009, slightly over a year after Russian forces defeated Georgia in a five-day war and declared it independent.
Culturally and religiously distinct from Georgians, Abkhaz separatists waged a fierce war after the Soviet Union`s collapse that killed thousands and caused some 250,000 people, mostly ethnic Georgians, to flee their homes.
The Black Sea region and South Ossetia, also declared independent by Russia following the August 2008 war, are still claimed by Georgia and not recognised by the West.
The region`s official representative in Moscow said Bagapsh had been suffering from lung cancer and had slipped into a coma after undergoing surgery on May 21.
Officials said he would be buried in his native village in Abkhazia on Thursday, with Medvedev attending a memorial service in Moscow on Monday.
Alexander Ankvab, Bagapsh`s deputy, has been appointed acting president, with new elections required by the region`s constitution within three months.
"We are deeply shocked by the death of Sergei Bagapsh," the acting head of Abkhazia told the Interfax news agency.
"This is a great loss for all the Abkhaz people."
The news was greeted with official silence from Georgia, whose US-backed President Mikheil Saakashvili faces almost daily street protests from pro-Russian opposition forces. (*)
Editor: Kunto Wibisono
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