Within Jerusalem’s holiest site, known as the Temple Mount to Jews and the Noble Sanctuary to Muslims, lies a historical question about what may be the world’s most contested piece of real estate.

The question, which many books and scholarly treatises have never definitively answered, is where on the 37-acre site, home to Islam’s sacred Dome of the Rock shrine and Al Aqsa Mosque, was the precise location of two ancient Jewish temples, one built on the remains of the other, and both long since gone.

Those temples are integral to Jewish religious history and to Israel’s disputed assertions of sovereignty over all of Jerusalem. Many Palestinians, suspicious of Israel’s intentions for the site, have increasingly expressed doubt that the temples ever existed — at least in that location. Many Israelis regard such a challenge as false and inflammatory denialism.

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“This is a very politically loaded subject,” said Matthew J. Adams, Dorot director of the W. F. Albright Institute of Archaeological Research in Jerusalem. “It’s also an academically complex question.”

Sacred to Judaism, Islam and Christianity, the world’s three great monotheistic religions, the site has been a perennial focal point for flare-ups in the Israeli-Palestinian conflict. Its history reflects the turbulent chronology of Jerusalem.

The city has been successively occupied for roughly 3,000 years by a parade of peoples, starting with the Canaanites and Israelites, then the Babylonians, Greeks, Persians, Romans, Byzantines, Muslims, Christian crusaders, Mamelukes, Ottomans, British and Jordanians.

The site has been administered by a special Islamic religious authority called the Waqf since the 12th century, after the legendary Muslim warrior Saladin conquered Jerusalem.

The Israeli authorities share security responsibilities with the Waqf and maintain a ban on non-Muslim prayer at the site. But pressure by nationalist religious Jews for access, including some calls for building a new temple, has aggravated Palestinian fears that the Israelis will change the current arrangement, an assertion the Israeli government denies.

Jewish scripture states that King Solomon built a temple around 960 B.C. on Mount Moriah and that it was destroyed by Babylonian invaders nearly four centuries later.

Although the biblical text does not specify the exact site of Mount Moriah, the Israeli scholar Rivka Gonen, in her book “Contested Holiness: Jewish, Muslim and Christian Perspectives on the Temple Mount in Jerusalem,” says the reference has been widely interpreted to mean the high point on the hill above the City of David — the rock now under the Dome of the Rock.

Many historians have said independent scientific verification of such a reference is problematic.

“The sources for the first temple are solely biblical, and no substantial archaeological remains have been verified,” said Wendy Pullan, senior lecturer in the history and philosophy of architecture at the University of Cambridge, in the book “The Struggle for Jerusalem’s Holy Places.”

Mr. Adams said, “We just don’t have enough primary source data, textual or archaeological, to say where it was with any confidence.”

Many historical texts say that Cyrus the Great of Persia, who conquered the Babylonians, let Jews rebuild the temple around 516 B.C., that King Herod added retaining walls about 37 B.C., and that Romans destroyed the rebuilt temple about 100 years afterward.

The Dome of the Rock, a shrine that is one of Islam’s holiest sites, was built at the highest point of the site around 691, which would be about 600 years after the second temple’s demise and 60 years after the Prophet Muhammad’s death, when Jerusalem was ruled by the Umayyad Dynasty during Islam’s Golden Age.

Many archaeologists agree that the religious body of evidence, corroborated by other historical accounts and artifacts that have been recovered from the site or nearby, supports the narrative that the Dome of the Rock was built on or close to the place where the Jewish temples once stood.

Nonetheless, the Waqf has never permitted invasive archaeological work that could possibly yield proof.

“That’s where you get to the Catch-22,” said Jodi Magness, a professor of religious studies at the University of North Carolina at Chapel Hill who was the consulting archaeologist in “Jerusalem,” a 2013 documentary film.

“The logical thing would be to dig,” Professor Magness said. “If you did that, you’d probably cause World War III to break out. It’s not even in the realm of possibility.”

Jane Cahill, an expert on Jerusalem’s early history who was a senior staff archaeologist for Hebrew University’s City of David Archaeological Project, said “nobody knows exactly” where the temples once stood, although “pretty powerful circumstantial evidence” suggests that they were on the site.

“Because there have been no organized excavations there, and not likely to be, circumstantial evidence is probably all we’re going to have,” she said.

Archaeologists agree that far more information is known that corroborates the existence of the second temple at the site than the first.

The historian Flavius Josephus, an eyewitness to Jerusalem in the first century, described the temple’s expansion under King Herod, surrounded by partition walls that were meant to separate gentiles and Jews. He also wrote about the temple’s destruction under the Romans.

An important piece of physical evidence supporting Josephus’s descriptions is a warning stone, written in Greek, admonishing visitors not to trespass into the partitioned area reserved for Jews. The stone, discovered in 1871 when Jerusalem was under the control of the Ottoman Empire, is on display at the Istanbul Archaeological Museum. It says any intruder “will invite death for himself.”

Further corroboration of the second temple’s existence on the site is in the New Testament, based on its account of anger at Paul by Jews who accused him of having violated the trespass restriction: “He has brought Greeks into the temple and defiled this holy place,” reads a passage from Acts 21:28.

The most direct physical evidence of the temple’s existence on the site is the Western Wall, an outer wall spared by Roman destruction. The wall has become a holy site in itself, drawing millions of Jews for prayer.

Kent Bramlett, a professor of archaeology and history of antiquity at La Sierra University in Riverside, Calif., said historical records of the destruction committed by the Romans, just by themselves, are “pretty overwhelming” in supporting the existence of the second temple in the immediate vicinity of the Dome of the Rock.

Still, he said, “I think one has to be careful about saying it stood where the Dome of the Rock stood.”

Ms. Cahill, who is also a practicing lawyer, said the answer to temple’s location depends partly on what constitutes proof. “The answer might be yes, if the standard of proof is merely a preponderance of the evidence, but no if the standard of proof is beyond a reasonable doubt,” she said.