The Interior Ministry earlier said the rebellion at the Mukhrovani tank base, 20 km from Tbilisi, was backed by Russia, as part of a plot to overthrow the Georgian leadership. Moscow denied the claim.
"The Georgian state did not yield to this provocation from Russia. This is an isolated incident - it did not spread to other military units, and the situation is under control," the president said.
Saakashvili said he personally negotiated with the rebel soldiers, and persuaded them to give themselves up to police.
He said the rebellion was aimed at "creating unrest in Georgia, to damage the country's security and democratic system."
The president accused Russia of conspiring with former Georgian military officials to stage the rebellion. The Interior Ministry said the mutiny was also aimed at disrupting NATO-led exercises due to start in the country on Wednesday.
A Kremlin official contacted by RIA Novosti declined to comment in detail on Saakashvili's allegations, but said the Georgian leader "needs to see a doctor".
A senior Russian security official called the reports a diversionary tactic to ease pressure on the government amid ongoing protests against Saakashvili.
The opposition, which has been leading protests in Tbilisi for nearly a month demanding Saakashvili's resignation, called the mutiny a "theatrical show" staged by Saakashvili.
"What we saw looked like a one-man theater show - one person giving specific names and painting an apocalyptic picture of men returning to Georgia from exile to kill long-serving politicians," David Gamkrelidze, an opposition leader, said.
Salome Zourabishvili, a former foreign minister who now leads the Georgia's Way party, called the government's reports "virtual reality." The Republican Party warned the government against "resorting to such methods to prevent the country from collapse."
However, the opposition said they had suspended pickets of the country's main highways, which were due to start on May 8.
The rebel battalion said in a statement earlier circulated by local media that they were not planning any military action, and urging for dialogue between the government and the opposition.
"Watching the country being torn apart by the current standoff is unbearable. There is a possibility of this standoff turning violent," battalion commander Col. Mamuka Gorgishvili was quoted as saying.
TV footage earlier on Tuesday showed heavy armored vehicles moving toward the base, and Saakashvili urging the personnel to surrender. The negotiations also involved Interior Minister Vano Merabishvili.
Police have barred reporters from approaching the base.
Saakashvili said Russia was trying to use the mutiny to target the upcoming NATO-led exercise as well as an EU summit in Prague designed to boost ties with ex-Soviet republics.
"Before these events, Russia tripled its military presence in Georgia in a bid to provoke unrest, which was aimed against democracy and Georgia's integration into Euro-Atlantic bodies," he said.
The Defense Ministry insisted that the schedule of the NATO drills would not be changed because of the incident.
The Interior Ministry said Russia's Black Sea Fleet was put on high alert after the rebellion. The Russian Navy denied the report, but border authorities said security had been tightened on the Georgian border.
Russia has criticized Western military alliance's planned drills in Georgia, saying that in view of last August's war over South Ossetia the exercises constitute "an open provocation" that could have negative repercussions.
The war followed Georgia's offensive on pro-Russian South Ossetia. The conflict is widely believed to have set back Georgia's bid to join NATO, which has been fiercely opposed by Moscow.