Under a deal signed by the French and Russian leaders last September, following the Russia-Georgia war, the EU was to deploy 200 monitors in Georgia. However, their mandate became a source of dispute after Russia recognized Georgia's breakaway republics - Abkhazia and South Ossetia - as independent states.
"I confirm that there would be no point in admitting an EU mission to Abkhazia, because we have observers and a mission from the United Nations. This is more than enough for us," Abkhaz president Sergei Bagapsh said during an interview on Russia Today's Spotlight program to be broadcast on Friday.
He said Abkhazia is "cautious" over admitting EU monitors, due to the EU's refusal to recognize Abkhazia as an independent country. However, he said the observers are still needed south of the border.
"Observers of the military situation are needed over there, where the aggression has been coming from for the past 20 years."
Bagapsh reiterated that Abkhazia refuses to negotiate with Georgian President Mikheil Saakashvili's regime.
"As far as Georgia's political actors and political leadership are concerned, we will have no contact with the current leadership," he said.
On February 13, the UN Security Council unanimously passed a resolution to extend the mandate for its observer mission in Georgia and Abkhazia by four months.
The UN mission in the Georgian-Abkhaz conflict zone - formerly known as the United Nations Observer Mission in Georgia (UNOMIG) - was deployed in 1993 to oversee a ceasefire following a post-Soviet conflict that resulted in Abkhazia gaining de facto independence.
Bagapsh said that Abkhazia will not seek recognition from any other countries.
"We are not going to ask anyone to recognize Abkhazia. We ourselves must work to create such a situation in the republic - economic and political stability, national unity - that will leave nobody with any questions," he said.
Russia recognized Abkhazia and South Ossetia after the five-day war with Georgia, which attacked South Ossetia in an attempt to bring it back under central control. Most residents of both Abkhazia and South Ossetia had held Russian citizenship for several years.
Russia's decision was condemned by the United States and the EU. Nicaragua has so far been the only other country to recognize South Ossetia and Abkhazia.