Administration and congressional officials said the hawkish Mr. Bolton is not expected to defer to the defense secretary; already, neoconservative members of the Republican foreign policy establishment have started to air concerns that Mr. Mattis is ceding strategic territory to Iran and Russia in Syria.

Mr. Mattis is widely viewed by global leaders as the strongest and perhaps most credible voice on foreign policy in an administration that has been rocked by firings and resignations among senior presidential advisers.