Bob Ballard’s exploration ship, the ­Nautilus, shown above, was anchored in Istanbul preparing for a two-month scientific expedition when the Turkish government asked for his assistance in its hunt for the U.S.-built F-4 and the two pilots. (NOAA Ocean Explorer)

Celebrated ocean explorer and Titanic finder Bob Ballard, working for the Turkish government, has located the bodies of two Turkish pilots shot down by Syria over the eastern Mediterranean last month, the Turkish military said in a statement released Wednesday.

Ballard and his crew aboard his research vessel Nautilus are now working to recover the remains, the statement said. Turkey did not disclose whether the bodies were found in Syrian or international waters, and a Ballard representative aboard the ship declined to comment.

After recovering the bodies, the Nautilus will resume its hunt for the wreckage of the F-4 jet downed by Syria on June 22, the Turkish military statement said.

The Nautilus was anchored in Istanbul preparing for a two-month scientific expedition when the Turkish government asked for Ballard’s assistance in its hunt for the U.S.-built jet and the two pilots.

Syria maintains the plane was within its airspace when it was shot down June 22, but Turkey disputes that. Territorial airspace extends 12 nautical miles offshore.

Debris, if found, could help settle the matter. If the plane was hit by antiaircraft gunfire, it was probably attacked within Syrian airspace, as such weapons have limited range, said a senior U.S. military official who spoke on the condition of anonymity because of the sensitivity of the issue.

But if the wreckage indicates that a missile downed the plane, then it could have been hit either in Syrian airspace or farther out to sea. The official said that U.S. intelligence reports have been “in­conclusive” on the location of the plane when it was hit and the type of weapon fired at it.

In an interview published in Turkey on Tuesday, Syrian President Bashar al-Assad said he regretted the incident. “We had absolutely no idea about the identity of the plane when we were shooting it down,” Assad said. “We do not even want to think that this plane was deliberately and purposefully sent into our airspace. We want to think that the pilot made a mistake.”

Turkey has said the aircraft was on a training mission and briefly and mistakenly entered Syrian airspace.

Turkish officials, after asking NATO allies for resources to help with the search, approached the Nautilus team via the U.S. Embassy in Ankara last week.

Ballard agreed to take on the mission, delaying a scientific expedition to explore the Black Sea and the eastern Mediterranean.

On Friday, the 211-foot Nautilus steamed out of Istanbul toward the Syrian coast, according to a statement from Turkey’s Foreign Affairs Ministry. The ship is now “under control of Turkey,” with Turkish officials onboard and directing the search, the statement read. Turkish naval ships are escorting the vessel.

A Ballard spokeswoman aboard the Nautilus, Liz Smith, said via e-mail that she could not provide details of the effort.

With powerful sonar and two remotely operated vehicles (ROVs) onboard, the Nautilus is equipped to find the jet’s wreckage, said Charles Royce, a veteran of similar searches as vice president of Oceaneering International, a Houston company that builds undersea remotely operated vehicles.

Ballard’s search is likely to have started near the last radar contact with the F-4, Royce said. Any such search begins by dropping sonar “towfish” into the water, which trail behind and scan the bottom.

Cutting swaths across the search area, the sonar towfish will hunt for a debris field — the same strategy that Ballard employed in the North Atlantic in 1985. There, he hit a historic jackpot: two enormous broken halves of the Titanic.

He’s now searching for a much smaller target. The F-4 probably shattered hitting the water, Royce said, breaking into “many, many, many pieces” that drifted to the bottom. “It can be very tedious,” he said. “You just go back and forth and make some guesses.”

If sonar picks up a trail of debris — and if it’s oriented in the direction the plane was headed on last radar contact — Ballard will splash an ROV to take a closer look, Royce said.

The two ROVs aboard Nautilus can send high-definition video of any wreckage back to the ship via a control cable.

Finding the remains of the two pilots would be much harder, Royce said.

The urgent mission is disrupting the plans of a rotating crew of 120 scientists, engineers and educators scheduled to work aboard the Nautilus this summer. Originally scheduled to begin July 1, the cruise was to search for ancient shipwrecks, explore an undersea volcano and gather samples of sea life.

The Turkish government has granted Ballard permits to conduct research in Turkish waters.

The search is being paid for by the Turkish government. A spokesman for the U.S. National Oceanic and Atmospheric Administration, which has provided funding to Ballard and his Institute for Exploration since 2005 said no NOAA funds were being used on the hunt for the jet.

With a full crew of 48, the Nautilus is expensive to operate, likely costing $70,000 to $100,000 a day, Royce said.

After agreeing to the mission, Ballard contacted NOAA and said, “When we’re done, we’ll pick up and do the mission we’re scheduled to do,” a NOAA spokesman said.

If anyone can find the wreckage, it’s Ballard and his experienced team, Royce said. The veteran explorer has led some 125 expeditions, scouring the oceans for famous wrecks. He located the German battleship Bismarck; the lost fleet of Guadalcanal; the remains of John F. Kennedy’s World War II war boat, PT 109, in the Solomon Sea; and the oldest shipwrecks ever found in deep water, off the coast of Israel. He launched the Nautilus in 2009.

The urgency of the Turkish request reflects both international tensions and domestic politics in Turkey.

The reluctance of NATO, the United States and other Western powers to intervene in Syria’s internal upheaval have been challenged by rising tensions between Syria and NATO-member Turkey along its border. The shoot-down led to Turkey calling for a NATO meeting to discuss invoking the alliance’s mutual defense pact.

Long-standing civil-military tensions inside Turkey have been exacerbated by media reports challenging the military’s conclusion that the plane had exited Syrian airspace long before it was struck.