WASHINGTON—The Obama administration and European and Arab allies are seeking to peel Russia away from its alliance with Iran, a partnership that has bolstered Syrian President Bashar al-Assad, said senior diplomats involved in efforts to end Syria’s lengthy conflict.

The efforts, which have unfolded quietly through meetings involving Russian President Vladimir Putin and Middle Eastern leaders, are meant to coax support from Moscow for a limit on Mr. Assad’s time in power. Such a step would solidify an emerging international...