Rudeinah's remarks come as US President Donald Trump's son-in-law and senior advisor Jared Kushner and special representative for global negotiations Jason Greenblatt are touring the Middle East to meet Arab and Israeli officials.
Kushner's direct appeal to the Palestinians - through an interview with the Palestinian Al-Quds newspaper published on Sunday - drew sharp criticism from several senior Palestinian officials.
Kushner and US Presidential senior envoy Jason Greenblatt are now visiting Israel as part of a regional tour to meet officials of Israel, Saudi Arabia, Qatar, Egypt and Jordan. They met with leaders of Israel, Jordan, Qatar, Egypt and Saudi Arabia to discuss the worsening situation in Gaza and proposals for a peace deal.
But Palestinians insist that the eastern part of Jerusalem will one day be the capital of their future state, a position supported by the worldwide community.
Senior Palestinian negotiator Saeb Erekat accused Kushner and Greenblatt on Saturday of trying to topple the Abbas-led West Bank autonomy government and dismantle the United Nations aid agency for Palestinian refugees. "He has his talking points which have not changed in the last 25 years".
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PLO Secretary-General Saeb Erekat said Kushner's interview "again illustrates the USA refusal to talk substance, to mention Palestinian rights or a Palestinian state".
"However, I do question how much President Abbas has the ability to, or is willing to, lean into finishing a deal".
It has always been an insurmountable sticking point, in the Palestinian view, that Jewish settlements built by Israel in the West Bank and East Jerusalem bisect what would become an independent Palestinian state.
The Israeli military said it responded with airstrikes Wednesday after some 45 rockets were fired toward Israel by Palestinian militants in Gaza.
The Duke of Cambridge is scheduled to meet both Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas.
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Medical sources at the Indonesian Hospital in Beit Lahia, in northern Gaza, said the soldiers shot two Palestinians with live fire, and two others with gas bombs, near the border fence in Abu Safiya area, east of nearby Jabalia, causing moderate wounds.
Kushner added that the Middle East peace plan is nearly completed, but did not elaborate on its details, the AP reported. Under these circumstances, American attempts to pressure Palestinians to accept the jaundiced peace plan are bound to backfire.
The trip comes as Israel celebrates the 70th anniversary of its foundation, and amid a rise in tensions between Palestinians and Israelis.
Israel said Thursday it has evidence the family of a baby who died near the Gaza border was paid by Hamas to accuse Israel's army over her death, an account the family rejected.
Al Jazeera's Harry Fawcett, reporting from West Jerusalem, said that the Palestinian leadership's reaction made it clear that there was "no prospect at this stage" that they want "anything to do with the U.S. administration or its plan, even ahead of its publication".
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The Health Ministry in Gaza Saturday unveiled a detailed official statistics on Palestinians killed and wounded by Israeli soldiers' gunfire since the outbreak of rallies and protests in Gaza Strip on March 30.