Qatari mediators have said they hope US pressure could help to achieve a deal, following a truce between Israel and Iran that ended the 12-day conflict between the countries.
On Sunday, Netanyahu told members of Israel's domestic intelligence agency Shin Bet that "victory" over Iran opened up many possibilities, "first and foremost, to rescue the hostages".
"Of course, we will also need to resolve the issue of Gaza, to defeat Hamas, but I believe we will achieve both missions. Beyond that, broad regional opportunities are opening up, in most of which - almost all - you are partners," he said.
Trump previously said he was hopeful a ceasefire in Gaza could be agreed in the next week.
In March, a two-month ceasefire collapsed when Israel launched fresh strikes on Gaza. It said it wanted to put pressure on Hamas to release its hostages.
Israel also imposed a total blockade on humanitarian aid deliveries to Gaza at the start of March, which it partially eased after 11 weeks following pressure from US allies and warnings from global experts that half a million people were facing starvation.
That partial easing included the creation of a US and Israeli-backed aid group, the Gaza Humanitarian Foundation (GHF), after Israel accused Hamas of stealing aid. Hamas has denied this.
GHF's aid system has been condemned by UN agencies. There have been repeated incidents of killings and injuries of Palestinians seeking aid.
Juliette Touma, communications director for the UN agency for Palestinian refugees, Unrwa, told the BBC that the new mechanism was "a killing field". She said the distribution of aid in an orderly way could only be done through the UN and other humanitarian organisations.
GHF boss Johnnie Moore previously told the BBC World Service's Newshour he did not deny deaths near aid sites, but said "100% of those casualties are being attributed to close proximity to GHF" and that was "not true".
The previous ceasefire deal between Israel and Hamas - which started on 19 January - was set up to have three stages, but did not make it past the first stage.
Stage two included establishing a permanent ceasefire, the return of remaining living hostages in Gaza in exchange for Palestinians imprisoned in Israel, and the complete withdrawal of Israeli forces from Gaza.
Trump has called for ongoing corruption charges against Netanyahu to be dropped, describing proceedings as a "political witch hunt" delaying ceasefire negotiations.
On Sunday, an Israeli court accepted a request by the Israeli prime minister to delay his scheduled testimony for a week, due to diplomatic and security issues.
Netanyahu was charged in 2019 with bribery, fraud and breach of trust, all of which he denies.
Earlier in the week, Israeli opposition leader Yair Lapid said Trump should not "intervene in a legal process of an independent state".
Israel launched its military campaign in Gaza in response to Hamas's 7 October 2023 attack, in which about 1,200 people were killed and 251 others were taken hostage.
Since then, 56,500 people have been killed in Gaza, according to the territory's Hamas-run health ministry.
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