For his actions in the North Caucasus, Abaev was awarded the Medal for Battle Merit and the Medal "For the Defence of the Caucasus". He was promoted to Sergeant in the 6th Guards Rifle Regiment of the 2nd Guards Rifle Division and became a squad leader. In November 1943, he fought in the Kerch–Eltigen Operation. On 2 November Abaev was reportedly among the first off the assault boat. A German machine gun prevented the advance to Height 63. Abaev reportedly killed the crew and turned the machine gun around on the German troops, enabling the capture of the Height. In two days he reportedly killed 32 German soldiers, nine in combat on Height 175. He also captured four other German soldiers. On 16 May 1944, he was awarded the title Hero of the Soviet Union and the Order of Lenin for his actions in Kerch.