Trump began a visit to the UAE on the latest stage of a tour of wealthy Gulf states after hailing plans by Qatar to invest $US10 billion ($A16 billion) in a US military facility during a trip to the country.
"I have absolutely no doubt that the relationship will only get bigger and better," Trump said in a meeting with UAE President Sheikh Mohamed bin Zayed Al Nahyan.
"Your wonderful brother came to Washington a few weeks ago and he told us about your generous statement as to the 1.4 trillion," Trump said, referring to a UAE pledge to invest $US1.4 trillion in the United States over 10 years.
Trump was referring to Sheikh Tahnoon bin Zayed Al Nahyan, Sheikh Mohamed's brother and the UAE's national security adviser and chairman of two of Abu Dhabi's deep-pocketed sovereign wealth funds.
"And all I can say is thank you very much," Trump added.
"We will work very hard to deserve it."
Sheikh Mohamed told Trump the UAE was "keen to continue and strengthen this friendship for the benefit of the two countries and peoples," adding to Trump: "your presence here today, your excellency, the president, confirms that this keenness is mutual."
Before his departure for the UAE, Trump said in a speech to US troops at the Al Udeid Air Base southwest of Doha that defence purchases signed by Qatar on Wednesday are worth $US42 billion.
He was met at the airport in Abu Dhabi by Sheikh Mohamed and the two leaders visited the Sheikh Zayed Grand Mosque, its white minarets and domes, impressive in the late-afternoon light.
"It is so beautiful," Trump told reporters inside the mosque, which he said had been closed for the day.
"First time they closed it. It's in honour of the United States. Better than in honour of me. Let's give it to the country. That's a great tribute."
The UAE's leaders want US help to make their wealthy Gulf state a global leader in artificial intelligence.
The US has a preliminary agreement with the UAE to allow it to import 500,000 of Nvidia's most advanced AI chips a year, starting this year, Reuters reported on Wednesday.
The deal would boost the UAE's construction of data centres vital to developing artificial intelligence models.
But the agreement has provoked national security concerns among sectors of the US government, and the terms could change, sources said.
At the presidential palace, Trump and Sheikh Mohamed could be seen in TV footage in conversation with Nvidia CEO Jensen Huang.
Trump said he would probably return to Washington DC on Friday after a regional trip that began on Tuesday, although he said it was "almost destination unknown - because they'll be getting calls 'could you be here? Could you be there?',".
Trump had hinted that he could stop in Istanbul for talks on Ukraine.
The two countries have finalised a technology framework agreement that was expected to be signed later on Thursday, a source with knowledge of the matter told Reuters.
The agreement requires commitments on both sides to the security of technology, the source said, without immediately providing details.
AI is likely to be a focus of the final leg of Trump's trip.
Former US president Joe Biden's administration had imposed strict oversight of exports of US AI chips to the Middle East and other regions.
Among the Biden administration's fears were that the prized semiconductors would be diverted to China and buttress its military strength.
Trump has made improving ties with some Gulf countries a key goal of his administration.
If all the proposed chip deals in Gulf states, and the UAE in particular, come together, the region would become a third power centre in global AI competition after the United States and China.
