( CNN) A U.S. proposal to deepen military cooperation with Russia in Syria has triggered a rift at the highest levels of the Obama administration, with the Pentagon openly challenging an idea that the top U.S. diplomat calls critical to moving Syria forward.

Even as Secretary of State John Kerry is in Moscow negotiating a possible agreement that could lead to the U.S. sharing classified intelligence with Russia over military ten-strikes both countries are conducting in Syria, the Pentagon is constructing it clear that Defense Secretary Ash Carter remains skeptical of Russian military activities in the war-torn country.