The US suspended Turkey from the F-35 program in mid-July over Ankara's purchase of Russia's S-400 air-defense system.

Russia has already made overtures about selling Turkey fighter jets, and on Tuesday at an air show in Moscow, the countries' presidents joked about just such a sale.

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Turkish President Recep Tayyip Erdogan and Russian President Vladimir underscored the close links between their countries at the opening of a major Russian air show on Tuesday.

Erdogan was Putin's guest of honor at the opening of the MAKS aviation show outside Moscow. The Turkish leader even got to peek inside the cockpit of Russia's newest fighter jet, the Su-57, which was unveiled at the show.

Turkey's military ties with Russia have been a cause of concern for NATO and the US after Ankara went ahead with its purchase of Russia's S-400 air-defense system despite warnings not to do so. The S-400 system began arriving in Turkey in mid-July, and Turkey's defense ministry said the second battery began arriving on Tuesday.

Russia's Su-57. Associated Press

The US says the Russian system is incompatible with NATO systems and poses a threat to the US-led F-35 program. It suspended Turkey's participation in the program in mid-July and has threatened sanctions against Ankara.

President Donald Trump expressed sympathy for Turkey, calling it a "very tough situation," but ultimately said the US would not sell the advanced fighter jet to Ankara. (The US Air Force chief of staff has not ruled out operating F-35s from Turkey, however.)

Shortly afterward, the head of Russia's state-run Rostech corporation said Moscow would be willing to sell Su-35 fighter jets to Turkey if Ankara "expresses interest," and on Tuesday, Putin appeared to say that the Su-57 was also on offer.

Russia recently began serial production of the Su-57, planning to build 76 of the fifth-generation fighter.

The Su-57 does have some advantageous features, like side-facing radar that enables it to trick the radar on US stealth fighters. But the Russian fighter jet largely relies on older fourth-generation engines and lacks the low-observable capabilities of other fifth-generation fighters, like the F-35.

Turkey had ordered 30 of the F-35, four of which had arrived and were at Luke Air Force Base in Arizona for training. Turkish pilots there were sent home after the US suspended Ankara from the program. Ten Turkish manufacturers were set to make more than 900 of the jet's components and would've made about $9 billion on F-35 parts contracts, according to the Defense Department.

Ellen Lord, the Pentagon's under secretary of defense for acquisition and sustainment, said on July 17 that it would cost the Defense Department between $500 million and $600 million to remove Turkey from the F-35 program but that the removal would have "minimal impact on the larger F-35 partnership."

"Turkey will certainly and regrettably lose jobs and future economic opportunities from this decision," Lord said.

The Associated Press contributed to this report.