looking for appropriate phrase

[tectonic-drift.livejournal.com]

I am looking for Russian phrases to substitute for the “I love you” that a mother or father would use when saying goodbye to their children. I have been told by a native speaker that a mother using the phrase “я люблю тебя, Наташа” to her daughter on an answering machine as farewell phrase is awkward. Would you agree? And, if so, can you help suggest some substitutes? Thanks.