She said he added that "the results of such a [military] action should be the entry of 30,000 Nato forces to deploy in Gaza" so as to prevent any further armed build-up.
Etinger would not say what Rice said in response.
The controversial leader of Yisrael Beiteinu became minister for strategic affairs after Ehud Olmert, the prime minister, signed a coaltion deal with the party last October.
"[Nato troops in Gaza] wouldn't provide a solution but rather worsen the problem."
Israeli deputy defence minister
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On being named to the cabinet in November he called for Israel to recapture part of Gaza.
Israeli forces left the Palestinian territory in 2005 after 38 years of military occupation.
Israel has generally objected to proposals to deploy foreign forces in Gaza or the West Bank, out of concern such a presence would limit its ability to pursue Palestinian fighters.
Efraim Sneh, the deputy defence minister from the left-wing Labour party, rejected Lieberman's idea.
Nato troops in Gaza "wouldn't provide a solution but rather worsen the problem" because Palestinian fighters would probably regard them as an enemy, just as they do Israel, Sneh told Israel Radio.