The U.S. and Russia engaged in talks Thursday to avoid crashes or other dangerous incidents over Syrian airspace, according to Russian officials, after the U.S. said the two nations' fighter jets came within close reach over the weekend.

The two sides are making progress, U.S. and Russian officials say.

Maj. Gen. Igor Konashenkov, a Russian defense ministry spokesman, said the jets came within 2 or 3 kilometers (1.2 to 1.8 miles) from the U.S. plane on Saturday, “not to intimidate, but to identify the object," according to the Wall Street Journal. U.S. Army Colonel Steve Warren described the distance apart as "miles," but did not clarify.

A senior U.S. military official told the Journal that the latest rounds of talks were inching close to a “memorandum of understanding” on how to stay out of each other’s way.

The official said a formal agreement could come within the coming days, but could just be a reiteration of a non-written agreement that both sides stay away from each other.

Russia’s air campaign has mostly focused on areas of western Syria, while the U.S.-led coalition has focused its target – the ISIS terror group – in Syria’s east.

However, the U.S. has repeatedly accused Russia of targeting U.S.-backed Syrian rebels in an effort to support Syrian President Bashar Assad. A U.S. official told Fox News on Wednesday that Moscow is “deliberately targeting” CIA-trained rebels.

"Putin is deliberately targeting our forces," a U.S. official, who is disappointed in the U.S. response to Russia, told Fox News.

"Our guys are fighting for their lives," said the official, estimating up to 150 CIA-trained moderate rebels have been killed by the Russians.

“Striking ISIL continues to be the least of Moscow’s priorities in Syria," said a U.S. intelligence official who also warned Putin might not look so tough if a Russian helicopter were downed or some Russian soldiers captured.

“In the modern age of social media, one captured Russian soldier paraded by extremists could shock the Russian population,” the official said.

Russia has called for other countries to join a coalition against “terrorist groups” in Syria. Russian Foreign Minister Sergei Lavrov criticized Washington Wednesday for refusing to consider more extensive cooperation in the sky over Syria.

“It’s hurtful,” Lavrov told the Russian parliament. He said a deal to avoid incidents is paramount, “but we are prepared to go much further, to coordinate much more deeply.”

A senior U.S. defense official said the talks with Russia officials are only to de-conflict airspace over Syria, and are not to discuss military coordination with the Russian military.

The U.S. believes Iranian-backed forces – predominantly Hezbollah operatives – are leading the Assad regime' fight near Aleppo in western Syria's Idlib province. Iranian and Syrian officials have long maintained that Iran has advisers and military experts in Syria. A U.S. official on Wednesday also told Fox News there is evidence from intelligence reports that Cuban paramilitary and special forces units are on the ground in Syria as well.

Russia began carrying out airstrikes in Syria on Sept. 30, and Syrian troops and allied militiamen began a ground offensive a week later.

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Fox News' Lucas Tomlinson, Jennifer Griffin and Doug McKelway and The Associated Press contributed to this report.