The finding has given rise to hope that the Judean Desert may yield more treasures, said Professor Chanan Eshel, an archaeologist from Tel Aviv's Bar Ilan University.
The two small pieces of brown animal skin, inscribed in Hebrew with verses from the Book of Leviticus, are from "refugee" caves in Nachal Arugot, a canyon near the Dead Sea where Jews hid from the Romans in the second century, Eshel said in an interview with The Associated Press.
The scrolls are being tested by Israel's Antiquities Authority. Recently, several relics bearing inscriptions, including a burial box purported to belong to Jesus' brother James, were revealed as modern forgeries.
More than 1,000 ancient texts - known collectively as the Dead Sea Scrolls - were discovered between 1947 and 1956 in 11 caves overlooking the western shores of the Dead Sea.
"No scrolls have been found in the Judean Desert" in decades, Eshel said. "The common belief has been that there is nothing left to find there."
Now, he said, scholars may be spurred on to further excavations.
Archaeologist and Bible scholar Steven Pfann said he had not seen the fragments. If authenticated, they would "in general not be doing more than confirming the character of the material that we have from the southern part of the Judean wilderness up until today."
But "what's interesting and exciting is that this is a new discovery," Pfann added. "This is the first time we've seen anything from the south since the 1960s."
Eshel said he was first shown the fragments last year during a meeting in an abandoned police station near the Dead Sea.
A Bedouin said he had been offered $20,000 for the fragments on the black market and wanted an evaluation.
The encounter that both excited and dismayed the archaeologist who has worked in the Judean Desert since 1986.
"I was jealous he had found it, not me. I was also very excited. I didn't believe I would see them again," said Eshel, who took photographs of the pieces he feared would soon be smuggled out of the country.
But in March 2005, he discovered the Bedouin still had the scroll fragments. Eshel bought them with $3,000 provided by Bar Ilan University and handed them over to the Antiquities Authority, he said.
"Scholars do not buy antiquities. I did it because I could not see it fall apart," Eshel said.
The finding constitutes the 15th scroll fragments found in the area from the same period of the Jewish "Bar Kochba" revolt against the Romans, and the first to be discovered with verses from Leviticus, Eshel said.
The Dead Sea Scrolls were written by the Essenes, a monastic sect seen by some as a link between Judaism and early Christianity. The scrolls comprise more than 1,000 ancient texts found a half century ago in the caves above Qumran in the West Bank, one of the most significant discoveries in the Holy Land.