"I do not regret the decision," he said on Wednesday. "For our country, this decision is irreversible."
Medvedev announced Russia's recognition of the two territories as independent on August 26 last year, in the wake of his country's war with Georgia over the regions.
Only the left-wing government of Nicaragua has joined Russia in recognising Abkhazia and South Ossetia's independence since then.
In Sukhumi, the Abkhaz capital, wreaths were laid on the graves of soldiers and a concert held on Wednesday evening, followed by a speech by separatist leader Sergei Bagapsh.
In South Ossetia, the main event was the dedication of a 160km pipeline to deliver gas directly from Russia to the region, cutting its reliance on pipelines passing
through Georgian-controlled territory.
Moscow said its recognition of the regions was part of a bid to protect Russian citizens in the two provinces, which split from Georgia after fighting in the early 1990s.
But Georgia has said last year's war and Russia's recognition amount to the seizure of its sovereign territory.
Abkhazia and South Ossetia continue to be beset by economic problems, despite injections of capital from Russia to rebuild the war-ravaged regions.
In South Ossetia, there has been mounting criticism over the slow pace of rebuilding amid allegations of corruption.
Both regions are home to thousands of Russian troops who patrol the borders with Georgia, where military tensions remain high.
War broke out between Russia and Georgia on August 7 2008, when Georgian forces launched an assault on South Ossetia following days of escalating violence.
Georgia, which insists the region remains an integral part of its territory, attempted to retake control of the region, including Abkhazia.
Russia fought back with a large-scale military operation into Georgia.
An EU-brokered ceasefire ended the conflict five days later, after several hundred people had been killed and thousands wounded.