Gela Bezhuashvili, secretary of the National Security Council, denied earlier reports that the device was thrown near the stage during Bush's appearance before a vast crowd on Tuesday and insisted that the US leader had not been in danger.
Bezhuashvili said the Soviet-era grenade was found 30m from the tribune where Bush spoke behind bulletproof glass.
US Secret Service spokesman Jonathan Cherry said on Tuesday that his agency was informed that a device, possibly a hand grenade, was thrown near the stage during Bush's speech, hit someone in the crowd and fell to the ground.
Bezhuashvili said, however, that it was not thrown; it was "found'.
"The goal is clear - to frighten or to scare people and to attract the attention of the mass media," he said.
"The goal has been reached, and that is why I'm talking to you now. In any case, there was no danger whatsoever for the presidents."
Bezhuashvili said the grenade was found in "inactive mode". He described it as an "engineering grenade" - one that is used for demolition or to simulate the effect of an artillery shell.
Such grenades' blast-effect can be fatal at close range; but unlike offensive grenades, they are not designed to spread shrapnel.
"I am not an expert, but it was not possible to detonate it there," Bezhuashvili said.
"The goal is clear - to frighten or to scare people and to attract the attention of the mass media ... In any case there was no danger whatsoever for the presidents"
Georgia security chief
However, military expert Tamas Khachidze disputed Bezhuashvili's description, saying the grenade was an RDG-5 combat hand grenade.
US embassy spokeswoman Khatiya Dzhindzhikhadze said the investigation would be handled jointly by American and Georgian specialists.
Security was tight at Freedom Square, where Bush and Georgian President Mikhail Saakashvili gave speeches before tens of thousands of people.
Georgian police were deployed and US snipers were visible on the rooftops, scanning the crowd with binoculars.
US agents and their Georgian counterparts manned the security gates at the square, making even Georgian performers - some of whom wore costumes with fake ammunition - remove every piece of metal before passing through the detectors.
Many in the crowd were carrying plastic bottles filled with water, which some high-spirited youths lobbed at each other during the speeches.
Parliament Speaker Nino Burdzhanadze accused unnamed forces of trying to sabotage US-Georgian ties, describing the grenade incident as a "provocative fact".
"There are many forces which are not interested in good relations between Georgia and the United States"
Georgia parliament speaker
"There are many forces which are not interested in good relations between Georgia and the United States," she told reporters, refusing to go into further detail.
Georgia's pro-Western leadership is locked in dispute with two breakaway regions, Abkhazia and South Ossetia, which have de-facto independence and close ties with neighboring Russia.
Russia's ties with Georgia have sharply deteriorated recently over stalled negotiations on the withdrawal of two Soviet-era bases from Georgian territory, seen in Tbilisi as a legacy of Moscow's historical domination of its smaller southern neighbour.