"We have not got a specific direction right now," said Joseph Votel, president of the US Central Command, which oversees US troops in the region, to journalists at the Pentagon via a teleconferencing conference.
Trump tweeted: "The summit with Russia was a big success, except for the real enemy of the people, Fake News Media. I look forward to our second meeting so we can start implementing some of the many things being discussed, including stop terrorism, security for Israel, nuclear weapons … ……… proliferation, cyber attacks, trade, Ukraine, Middle East, North Korea and more. There are many answers, some simple and a bit difficult for these problems … but they can all be solved! "
Votel said he was" not privileged "to any talks between the US, Russia and Israel that would strive to pull down the American forces in Syria in exchange for Russian guarantees to keep Iranian forces and Iranian support groups away from the border between Israel and Syria.
"I'm not insulting any kind of grand bargain discussion or anything like that," said Votel.
He also noted that the US military is prohibited by law from coordinating, synchronizing or cooperating with Russian forces.
Following the Russian military invasion 2014 in Ukraine and its seizure in the Crimean Congress banned "something bilateral military for military cooperation" with Russia in its passage of the Defense Forces Act.
Votel said that any cooperation "would have to be created by the congress or an exception that they would approve to allow us to do something like that. I have not requested it right now and we will see which direction comes down."  On Tuesday, a spokesman for the Russian Ministry of Defense said Russia was ready to enter into agreements with Trump and Putin "on international security", including issues of "cooperation in Syria".
White House and Pentagon would not confirm any agreements had been made or offer any details.
"When we can provide more details, we will, but insure us that the US Department of Defense is still laser focused on the defense of our nation, chief Pentagon spokesman Dana White told CNN late Wednesday.
The National Security Council would not confirm what Trump had agreed on in his one-on-one with Putin. A NSC spokesman told CNN on Tuesday that they are still "reviewing the discussion."
The US military is making "de-conflict" with Russian forces in Syria as part of an attempt to avoid accidents that both the United States and Russian militants seem relatively close to each other there.
Votel said the deflam hotline in Syria has "remained a professional exchange."