The 27-year-old goalie is entering the final year of a four-year contract and could have become an unrestricted free agent after the season. Kochetkov was limited to nine games (eight starts) last season and went 6-2-0 with a 2.33 goals-against average, .899 save percentage and one shutout, last playing Dec. 20 before having hip surgery.
Kochetkov was healthy enough to dress as the Hurricanes backup behind Brandon Bussi during the Stanley Cup Final after Frederik Andersen was injured, but did not play in any games.
"Pyotr is an incredibly talented goalie whose aggressive style fits our team very well," Hurricanes general manager Eric Tulsky said. "We believe in his ability to win games for this organization and are thrilled he wants to continue helping us pursue championships in Carolina."
Selected by Carolina in the second round (No. 36) of the 2019 NHL Draft, Kochetkov is 71-38-12 with a 2.46 GAA, .905 save percentage and 11 shutouts in 125 games (120 starts) and 2-5 with a 3.83 GAA and .860 save percentage in 10 Stanley Cup Playoff games.