"The Civil Nuclear Deal (There will be no enrichment of material!)... which pertains only to non-military use... will be approved, but is totally subject to Saudi Arabia joining the very respected and successful Abraham Accords," Trump said in a post on Truth Social.
Trump's remarks come after criticism from experts that the deal could run the risk of future nuclear proliferation in an already unstable region.
Saudi Arabia has previously said it would not recognise Israel without the establishment of a Palestinian state.
In 2020, Trump brokered the Abraham Accords, which secured the historic normalisation of relations between Israel and two Arab nations, the United Arab Emirates (UAE) and Bahrain.
Sudan, Morocco and Kazakhstan have since also signed the accords.
Saudi Arabia has not so far responded to Trump's remarks.
And it was not immediately clear if the condition of joining the Abraham Accords was stipulated in the text of the deal - which has not been released - or that Saudi Arabia had agreed to that condition, or would be forced to join the accords.
Meanwhile Israel welcomed Trump's statement.
Posting on X, Prime Minister Benjamin Netanyahu's office said Saudi Arabia joining the accords "would be an historic leap forward for peace in the Middle East".
The statement did not mention the nuclear deal. However, Israeli Economy Minister Nir Barkat said previously his country "can manage it" if Saudi Arabia had nuclear power for peaceful means.
Israel itself is widely believed to have nuclear weapons, but it neither confirms nor denies that this is the case.
The US-Saudi deal, whose signing was announced on Wednesday, is described as a "peaceful nuclear co-operation agreement" that will provide "great access for American companies in the Saudi nuclear energy programme" by the US energy department.
The nuclear issue has been at the centre of the months-long US-Israeli conflict with Iran.
Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman, told CBS News in 2018 that his own nation was not planning to acquire a nuclear weapon, but that "without a doubt if Iran developed a nuclear bomb, we will follow suit as soon as possible".
Earlier US media reports suggested the deal could allow Saudi Arabia to enrich uranium in the future - which can be used as fuel for power plants, but also potentially to make nuclear bombs. However, Trump's remarks appear to deny this.
The agreement will now be sent to the US Congress for review.
Some lawmakers on both sides of the political aisle are expected to oppose the deal, though Trump's Republican Party controls both the upper and lower chambers and opponents of the deal do not appear to have the votes needed to block it.