The disagreement is over the "San Jose," a treasure ship wreck that Colombia located recently off the coast of Cartagena de Indias, its old Caribbean port city.
The "San Jose" sank in June 1708 near the Islas del Rosario, during combat with British ships attempting to take its cargo, as part of the War of Spanish Succession.
The Spanish galleon was the main ship in a treasure fleet carrying gold and silver - likely extracted from Spanish colonial mines in Peru and Bolivia - and other valuables to King Philip V.
President Juan Manuel Santos announced in early December that experts had found the "San Jose" on November 27th in a place never searched before.
So who owns the estimated $2 billion in loot?
"There are discrepancies on the issue of legal ownership," said Spain's Foreign Minister José Manuel García-Margallo.
He met on Saturday with his Colombian counterpart María Angel Holguin in Cartagena.
Spain in part has based its arguments on UN Law of the Sea rules. But Colombia is not a signatory to the treaty, and as such is not subject to those regulations.
The Spanish diplomat said that he was hoping a "roadmap for an understanding" could be hammered out given the countries' excellent relations.
"This is not going to become an issue that divides us," Holguin stressed, while acknowledging legal disagreements remained.
Only a handful of the ship's crew of 600 survived when the "San Jose" sank.
Treasure hunters had searched for the ship, described by some as the holy grail of wrecks, for decades.
A team of Colombian and foreign researchers, including a veteran of the group that discovered the wreck of the Titanic in 1985, studied winds and currents of the Caribbean 307 years ago and delved into colonial archives in Spain and Colombia searching for clues.
The loot is estimated to be worth at least $2 billion, its value having dropped significantly due to the falling price of silver, according to US-based company Sea Search Armada.
SSA, whose subsidiary claimed in the early 1980s that it had found the galleon's final resting place, was engaged in a long-running battle with the Colombian government.
The find was not confirmed and a US court ultimately ruled it was Colombian property.
Colombia, not surprisingly, agreed.