Israeli Prime Minister Benjamin Netanyahu said the mother and daughter were abducted by Hamas while they were staying at Kibbutz Nahal Oz.
Israelis are still reeling from the Hamas assault and from images of fellow citizens being bundled off to Gaza, which is ruled by Hamas.
An attempt to rescue all those Hamas said were now held in different locations could jeopardise their lives.
American and British officials said they have been working with Qatar to secure the release of hostages, including their citizens, held in Gaza.
Israel has also said that there will be no end to its full blockade of the enclave unless Israeli hostages are freed.
Persons:
Judith Tai Raanan, Natalie Shoshana Raanan, Israel, Benjamin Netanyahu, Natalie Raanan's, Ben Raanan, Judith Raanan's, Netanyahu, Joe Biden, Yonatan “ Yoni ” Netanyahu, Izz, Deen al, Abu Ubaida, Joe, Biden, Mia Schem, Gilad Shalit, Enas Alashray, Nidal, Michael Georgy, Steve Gorman, Grant McCool
Organizations:
Kibbutz, Denver Post, Gaza, Media, Hamas, Air, Qatar, Thomson
Locations:
GAZA, Chicago, Israel, Denver, Qatar, United States, Evanston, an Illinois, Gaza, Entebbe, Uganda, Air France, Palestinian, Thailand, Argentina, Germany, France, Portugal, Hamas, Cairo