An unusual dispute is flaring between a Texas energy firm and the state-owned oil company of Georgia, a battle that combines elements of corporate intrigue, international law and U.S. national security.

On one side is Georgia, a U.S. ally and NATO partner that signed an oil exploration contract with the Texas company in the mid-1990s, soon after gaining independence from the Soviet Union.

The opposing party is Frontera Resources, an oil and gas firm founded by former Houston Mayor and U.S. deputy energy secretary Bill White. Frontera has faced financial problems and was last year delisted from the London Stock Exchange, while its activities in Georgia have been “dogged by controversy.”

The relationship has blown up in acrimony, with Georgian officials accusing Frontera of failing to honor a recent international arbitrator’s ruling stemming from a contract dispute in which the Caucasus nation prevailed. The Georgian Oil & Gas Corp. has terminated the contract.

“Frontera has engaged in an unprecedented attack against the Georgian Government and the Georgian people,” George Bakhtadze, the Georgian co ...