Rubio arrived hours after Hamas freed three Israeli captives in Gaza in exchange for 369 Palestinian prisoners -- the sixth swap under the Gaza ceasefire between Israel and Hamas.
Negotiations on a second phase of the truce, aimed at securing a more lasting end to the war, are expected to begin next week in Doha.
The following statements were taken from AFP's coverage of the joint news conference in Jerusalem:
"Hamas cannot continue as a military or a government force... they must be eliminated," US top diplomat Rubio said in the joint news conference with Israeli PM Netanyahu by his side.
"We discussed Trump's bold vision for Gaza's future and will work to ensure that vision becomes a reality," Netanyahu told reporters after the meeting, referring to US President Donald Trump's proposal to take control of Gaza and ethnically cleanse the native population from the strip and deport 2.4 million Palestinians to Egypt and Jordan.
"We have a common strategy, and we can't always share the details of this strategy with the public, including when the gates of hell will be opened, as they surely will if all our hostages are not released until the last one," Netanyahu said in the joint statement adding: "We will eliminate Hamas's military capability and its political rule in Gaza."
Rubio replied: "The president's also been very bold about his view of what the future for Gaza should be, not the same tired ideas of the past, but something that's bold and something that, frankly, took courage and vision... what cannot continue is the same cycle."
The United States, Israel's top ally and weapons supplier, has said it is open to alternative proposals from Arab governments but insists that, for now, "the only plan is Trump's."
Rubio said he believed Arab states were "working in good faith" but insisted Hamas must have no future role.
Egypt, Jordan, and the Arab League reaffirmed their categorical rejection of the recent US/Israeli proposals for the ethnic cleansing of the Gaza Strip.
In tandem, Egypt is set to announce a comprehensive plan for the immediate reconstruction of the strip without displacing the native population.
Egypt is set to host an emergency Arab Summit on 27 February to formulate a unified Arab response against US-Israeli plans for Gaza.
Cairo supports empowering the Palestinian Authority to govern a unified Palestinian territory, including Gaza and the West Bank, toward the establishment of an independent State of Palestine as part of a two-state solution.
Earlier on Saturday, an informed Egyptian source told Al-Qahera News TV channel that Hamas said it would not participate in the administration of the Gaza Strip in the upcoming phase.
Qasim's statements come hours after Israel and Hamas completed swapping the sixth batch of prisoners under the ceasefire deal brokered by Egypt, Qatar, and the US, which went into effect on 19 January.
The recent Hamas statements come as the Palestinian group reaffirmed its commitment to abiding by the terms of the ceasefire deal while asking mediators to pressure Israel to halt its violations of the agreement.
Lebanon
On Lebanon, Netanyahu said: "Hezbollah must be disarmed. And Israel would prefer that the Lebanese army do that job, but no one should doubt that Israel will do what it has to do to enforce the understandings of the ceasefire and defend our security,"
Aligning with Netanyahu, Rubio said: "In the case of Lebanon, our goals are aligned in the same. A strong Lebanese state that can take on and disarm Hezbollah."
Syria
On Syria, Rubio said: "While the fall of Assad is certainly promising and important, Syria replacing one destabilising force for another is not a positive development, and that is something that we will watch very carefully," referring to the December toppling of president Bashar al-Assad by Islamist-led militants.
Netanyahu threatened: "Israel will act to prevent any threat from emerging near our border in southwest Syria," adding that "if any force in Syria today believes that Israel will permit other hostile forces to use Syria as a base of operations against us, they are gravely mistaken."
Iran
Netanyahu said Israel would "finish the job" against Iran with US support, adding "Israel and America stand shoulder to shoulder in countering the threat of Iran."
"Over the last 16 months, Israel has dealt a mighty blow to Iran's terror access under the strong leadership of President (Donald) Trump and with your unflinching support, I have no doubt that we can and will finish the job," Netanyahu said.
Rubio, describing Iran as the"single greatest source of instability in the region," asserted: "There can never be a nuclear Iran, a nuclear Iran that could then hold itself immune from pressure and from action. That can never happen."
The remarks on Iran come as Netanyahu has been looking to shore up support in the US for an attack on Iran's nuclear facilities. Tehran has insisted its nuclear program is for civilian purposes.
Off to UAE and Saudi Arabia
Rubio will leave Tel Aviv for the United Arab Emirates (UAE) and Saudi Arabia.
"Rubio’s engagements with senior officials will promote U.S. interests in advancing regional cooperation, stability, and peace,” stated the US State Department. "The trip will centre on freeing American and all other hostages from Hamas captivity, advancing to Phase II of the ceasefire agreement in Gaza, and countering the destabilizing activities of the Iranian regime and its proxies.”
The UAE, key in the 2020 Abraham Accords – where four Arab states normalized relations with Israel – has rejected Trump's displacement proposals.
In tandem, Saudi Arabia has reaffirmed that it will not normalize relations with Israel without a pathway to a Palestinian state.
Saudi Arabia will host leaders from Egypt, Jordan, Qatar and the UAE in Riyadh on 20 February ahead of Cairo’s summit to discuss alternatives to Trump’s Gaza plan a source told AFP.
Another source said Palestinian Authority president Mahmoud Abbas is expected to attend.
Arab countries have presented a united front, condemning the mass displacement of Palestinians as a threat to regional security and an attempt to erase the Palestinian cause.
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