Israeli forces pressed on with a raid into Gaza's southern area of Khan Younis after ordering civilians to evacuate some districts they said had been used for renewed attacks by Palestinian militants.
Thousands of people were fleeing for safer areas as Israeli airstrikes hit, UN officials said.
Netanyahu is currently in Washington and is expected to meet US President Joe Biden later this week after making an address to Congress.
Speaking in the US capital on Monday to families of hostages, he said: "The conditions (for a deal) are undoubtedly ripening. This is a good sign."
Efforts to reach a ceasefire in the war between Israel and Hamas, outlined by Biden in May and mediated by Egypt and Qatar, have gained momentum over the past month.
"Unfortunately, it will not take place all at once; there will be stages. However, I believe that we can advance the deal and leave us in possession of the leverage to bring about the release of the others (hostages not freed in first stage)," Netanyahu said.
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