Muravyov took part in an expedition to the eastern shore of the Caspian Sea, negotiated with the Khan of Khiva on trade between the khanate and Russia (1819–20).

[1] Muravyov fought well at Akhaltsikhe in the Russo-Turkish War (1828–29) and distinguished himself during the battle of Warsaw (1831) of the November Uprising.

Continuing to serve in the military, he took active part in the fights of the Crimean War, being Namestnik and commander of the Separate Caucasus Corps (11.12.1854–3.8.1856).

On his arrival in the Caucasus, in a letter to the general of the Infantry Yermolov he accused the Caucasian troops of loss of fighting spirit and "disorder, rooted in many years of careless management" (the letter and a polemical anonymous response to it by Prince D. I. Svyatopolk-Mirsky soon became public).

Instead of "formidable expeditions" against the highlanders, which, in his opinion, had no real result, he advocated increased colonization of the occupied territories.