Dubai - The phone call was based on coordination of Trump who had earlier talked with Sheikh Tamim.
The nations say Doha supports regional foe Iran and militants, charges Qatar's leaders deny. Kuwait has been trying to mediate the dispute.
"During the call, the Amir of Qatar expressed his desire to sit at the dialogue table and discuss the demands of the four countries to ensure the interests of all," Saudi state news agency SPA reported.
"The details will be announced later after the Kingdom of Saudi Arabia concludes an understanding with the United Arab Emirates, the Kingdom of Bahrain and the Arab Republic of Egypt," SPA said.
The phone call was the first publicly reported contact between the two leaders since the start of the crisis.
Qatar's state news agency QNA said the phone call was based on coordination of US President Donald Trump who had earlier talked with Sheikh Tamim.
Trump on Thursday said he would be willing to step in and mediate the worst dispute in decades among the US-allied Arab states and Qatar, and said he thinks a deal could come quickly.
Both Qatar Amir and the Saudi Crown Prince "stressed the need to resolve the crisis by sitting down to the dialogue table to ensure the unity and stability of the GCC countries," QNA reported.
Sheikh Tamim welcomed the proposal of Prince Mohammed during the call "to assign two envoys to resolve controversial issues in a way that does not affect the sovereignty of the states," QNA said.
Saudi Arabia later issued a second statement citing an unnamed official at the ministry of the foreign affairs denying the QNA report.
"What was published on the Qatar News Agency is a continuation of the distortion of the Qatari authority of the facts," SPA reported citing the Saudi official.
"The Kingdom of Saudi Arabia announces the suspension of any dialogue or communication with the authority in Qatar until a clear statement is issued clarifying its position in public."