Archeologists digging in the dirt and black ooze under Mexico City's most important public square have been tantalized for decades by the possibility of a great treasure and likely burial place of one of the last Aztec rulers.

"They keep finding astonishing things as they inch their way along," says David Carrasco, a Harvard University historian who's worked with Mexican archeologists at the Templo Mayor.

But the great find – a royal tomb – has eluded scientists. The city of Tenochtitlan, the Aztec capital that lies beneath the modern Mexico City, was founded on an island in the middle of a saltwater lake.

A high water table makes progress difficult. "When you dig a pit or a trench, you find very quickly the water level and cannot continue if you don't have a powerful pumping system," says Leonardo Lopez, the archeologist heading the excavation.

Since he uncovered a carved monolith of the ferocious earth deity Tlaltecuhtli in 2006, there has been intense speculation, based on historical writings and their own discoveries, that the four-metre-by-3.5-metre stone covers a royal tomb.

The stone monolith is inscribed with dates and language associated with Ahuitzotl, a king who died in 1502. Radar indicates "anomalies" under the monolith, which could be funerary spaces.

Though archeological finds in Mexico City date back to 1790, no one has ever found the burial site of an Aztec king.

"Everyone wants us to dig faster," says Lopez, "and this is the only thing we cannot do.

"You can only excavate once an archeological site. We are not treasure hunters but scientists, and we have a professional responsibility to record the slightest artifact in the best way."

Still, they have uncovered the kinds of treasures that excite public interest, including a canine figure, possibly a dog, with turquoise earplugs, jade necklace and a golden bell around its feet.

A collection of 14 hammered gold ornaments – rare finds in large caches – never before on public display will be part of an exhibit on Moctezuma II opening in September at London's British Museum.

"This monolith is one of the great Aztec deities," says Carrasco. "Imagine what she meant to them, and they buried it. (Today) in the middle of the old city, the national cathedral, the presidential palace, the supreme court are nearby – all this great symbolism, on this spot, the centre of Mexico since pre-Columbian times."

Archeologists anticipate discovering a storehouse that will help them understand Mexica (as the Aztec people are known) funerary practices as well as the economic and political power in the years leading up to 1519, when Spanish conquerors razed the Templo Mayor pyramid complex.

"We expect to find the cremated remains of one or more kings, servants, dwarfs, albinos, musicians sacrificed during the funerals, a rich offering of jewels," says Lopez, who has worked on the excavation since 1978.

On one side of the monolith, Lopez found an entrance. "Digging deeper we have detected several plaster seals blocking the way, meaning that the place below is not looted." The ornamental dog may represent the dog the Mexica believed help the dead arrive at the underworld, he says.

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While records refer to Ahuitzotl and two other kings buried at Templo Mayor, says Lopez, there's no likelihood the remains of Moctezuma II, the last great Aztec kings, will be found.

"Moctezuma II died in a very difficult moment and his body was not the object of a royal funeral. A source says this his body was cremated inside a burned temple and that immediately after a group of followers drank his ashes."