His remarks come after Moscow last week proposed plans to Washington to cooperate on the safe return of refugees to Syria following a meeting between President Donald Trump and his Russian counterpart Vladimir Putin in Helsinki.
On Friday, Secretary of State Mike Pompeo confirmed the issue had been discussed by the two presidents.
However, US defense officials are shocked at the prospect of coordinating with Russia in Syria, where the two countries are conducting two separate military campaigns.
Russia is in Syria at the request of the government of Bashar al-Assad to help fight Daesh, while Washington and its allies have been launching attacks on Syria since 2014, claiming they seek to root out the terrorist group, but they are also aiding militants fighting the government.
Now, the Pentagon, which blames Russia for conditions that caused refugee flows in the first place, says coordination between the two countries requires special permission from Congress.
Presently, the only coordination between the US-led coalition with Russia in Syria is through a special hotline to insure there are no mishaps involving the two sides’ ground forces or planes.
“We will not be doing anything additional until the Secretary of State and the president have further figured out at what point we are going to start working, alongside our allies, with Russia in the future,” Mattis said at a press conference in California on Tuesday.
“That has not happened yet. And it would be premature for me to go into any more detail at this point, because we’re not doing any more than this,” he added.
Meanwhile, General Joe Votel, the top commander overseeing US military involvement in Syria, said on Thursday no new instructions were issued regarding cooperation with Russians since Trump’s summit with Putin.
Congress passed a law banning military-to-military cooperation following the rejoining of Crimea with Russia in 2014.
Crimea decided to join Russia and two provinces in the east revolted by establishing self-declared republics.