Kivlenieks was first selected to the senior Latvian national team, serving as the third-string goaltender at the 2018 IIHF World Championship. He later made his World Championship debut with Latvia as the host country of the 2021 IIHF World Championship. Kivlenieks was used as the starting goaltender as he led Latvia to its first ever win over Canada and also its first loss against Kazakhstan during the group phase.