Clutterbuck (two years) and Parise (one year) each could have become an unrestricted free agent after the season.
"Obviously I'm thrilled to sign an extension and have that dealt with," Clutterbuck said. "Especially this time of the year, it can be a stressful time so I'm just thankful that this has gotten done and we don't have to worry about. I'm thrilled to be here for a couple more years with these guys and this organization. Obviously, it's home for me, so I'm thrilled."
Clutterbuck, a 34-year-old forward, is in the final season of a five-year contract he signed with the Islanders on Dec. 9, 2016. He has scored 15 points (six goals, nine assists) in 59 games.
Selected by the Minnesota Wild in the third round (No. 72) of the 2006 NHL Draft, Clutterbuck has scored 262 points (130 goals, 132 assists) in 933 regular-season games for the Islanders and Wild and 19 points (11 goals, eight assists) in 70 Stanley Cup Playoff games.
"I don't think we looked at keeping 'The Identity Line' (of Clutterbuck, Casey Cizikas and Matt Martin) intact, we looked at it as keeping Cal here," Islanders general manager Lou Lamoriello said. "He certainly has been one of our, if not one of our best, penalty killers over the years. He's stayed pretty much healthy, takes care of himself, and I think we all know the game that he plays. There's a good reason why a lot of teams were extremely interested in him at this period of time, because he is a playoff-type of performer."
Parise, a 37-year-old forward, signed a one-year contract with the Islanders before the season. He has scored 24 points (eight goals, 16 assists) in 60 games.
"I had a slow start statistically, I thought I was trying to get comfortable at the beginning of the year. But I still didn't mind the way I was playing," Parise said. "The second half, things have started to come a little easier, a little more natural for me. … I'm looking forward to continuing that the rest of the season and into next year."
Selected by the New Jersey Devils with the No. 17 pick of the 2002 NHL Draft, Parise has scored 834 points (401 goals, 433 assists) in 1,120 regular-season games with the Islanders, Devils and Minnesota Wild, and 80 points (37 goals, 43 assists) in 105 playoff games.
The Islanders (26-25-9) are sixth in the Metropolitan Division.
NHL.com deputy managing editor Brian Compton contributed to this report
