My condolences

Мои соболезнования (употребляется также с издёвкой);
Приношу (примите) мои соболезнования; Сочувствую; Я тебе сочувствую.

Wiktionary: comfort, support, or sympathy offered to the family and friends of somebody who has died.

Example: I sent her a card expressing my condolences after her mother passed away.

Example: We offer our sincere condolences to Tabatha and her family.