Israel and Hamas have agreed to a first phase of a peace deal brokered by the US president, with a ceasefire taking effect on Friday.
Dr Naim said the ceasefire would not have been possible without President Trump, but insisted he needed to continue to apply pressure to Israel to stick to the agreement.
He added that Hamas would be willing to step aside for a Palestinian body to govern a post-war Gaza, but that they would remain “on the ground” and would not be disarmed.
Dr Naim said in the interview: “Without the personal interference of President Trump in this case, I don’t think that it would have happened to have reached the end of the war.
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“Therefore, yes, we thank President Trump and his personal efforts to interfere and to pressure Israel to bring an end to this massacre and slaughtering.”
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He added: “We believe and we hope that President Trump will continue to interfere personally and to exercise the maximum pressure on [Israeli Prime Minister Benjamin] Netanyahu to fulfil its obligation.
“First, as according to the deal, and second, according to the international law as an occupying power, because I think without this pressure, without this personal interference from President Trump, this will not happen.
“We have already seen Netanyahu speaking to the media, threatening to go to war again if this doesn’t happen, if that doesn’t happen.”
Image: Donald Trump has been thanked for his role in securing a peace deal in Gaza. Pic: AP
Questions remain over the next phases of the peace plan, including who will govern Gaza as Israeli troops gradually pull back and whether Hamas will disarm – as called for in Mr Trump’s ceasefire plan.
Mr Netanyahu has hinted that Israel might renew its offensive if Hamas does not give up its weapons.
However, Dr Naim said Hamas would not completely disarm and that weapons would only be handed over to the Palestinian state, with fighters integrated into the Palestinian National Army.
“No one has the right to deny us the right to resist the occupation of armies,” he said.
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Thousands of Gazans are heading north as Israeli troops pull back.
On future governance, Dr Naim criticised plans for Sir Tony to play any role in overseeing the future of Gaza, saying that Hamas and Palestinians were angered by his role in previous wars in Afghanistan and Iraq.
Dr Naim added: “When it comes to Tony Blair, unfortunately, we Palestinians, Arabs and Muslims and maybe others around the world have bad memories of him.
“We can still remember his role in killing, causing thousands or millions of deaths to innocent civilians in Afghanistan and Iraq.
“We can still remember him very well after destroying Iraq and Afghanistan.”
Under Mr Trump’s plans, Sir Tony would form part of an international supervisory body.
The international body, the Council of Peace or Board of Peace, would govern under plans approved by Mr Netanyahu.