The White House said Trump discussed the issue on Wednesday in a telephone conversation with Saudi Arabia's King Salman.
Trump told King Salman that a diplomatic resolution would fulfil a commitment - made when Trump visited Riyadh - to maintain unity while fighting "terrorism".
Analysts say the Trump administration is concerned about Qatar's growing relationship with Iran as a result of the ongoing crisis.
"We need to see this within the context of Qatar making a decision about one week ago to return its envoy to Tehran after nearly 21 months of him been pulled back to Doha," Giorgio Cafiero, CEO of Gulf State Analytics, a geopolitical risk consulting firm, told Al Jazeera.
"The trump administration is very concerned about something that's going on in the Gulf - that is the growing relationship between Qatar and Iran as a consequence of the current crisis in the GCC," Cafiero said.
"We welcome all initiatives to resolve the Gulf crisis, and we support the Kuwaiti efforts in that direction," Russia's foreign minister Sergey Lavrov said during a joint press conference in Doha with his Qatari counterpart, Sheikh Mohammad bin Abdelrahman Al Thani.
Lavrov, who will visit Saudi Arabia and Jordan in September, said the only way to resolve the crisis is through negotiations and dialogue between all parties.
The diplomatic crisis began in June, when Bahrain, Egypt, Saudi Arabia and the United Arab Emirates cut ties to Qatar over allegations that it was funding "extremists" and was too close to Iran. Qatar has denied the allegations.
Source: Al Jazeera and news agencies