Saudi Arabia's Crown Prince Mohammed bin Salman spoke by with Qatar's Emir Sheikh Tamim bin Hamad al-Thani on Friday when they discussed the dispute, state media from both countries reported.
According to a White House statement, Trump told the three Persian Gulf Arab rulers that unity among Washington's Arab partners to promote regional stability and counter "the threat of Iran".
"Setting preconditions for dialogue confirms Qatar's lack of seriousness in dialogue, combating and financing terrorism and interfering in the internal affairs of countries", the bloc said in its statement.
The recent Gulf crisis began in June 5 when Saudi Arabia, Bahrain, Egypt, and the UAE all cut ties to Doha over allegations that Qatar funds extremists and has ties that are too warm with Iran.
The report stated that Prince Mohammad welcomed the proposal saying that after a mutual agreement with the United Arab Emirates (UAE), Egypt and Bahrain is made, further details will be revealed.
US President Donald Trump's attempt to cool escalating tensions between Saudi Arabia and Qatar has ended up in failure this week as the two Arab kingdoms release conflicting statements shortly after a phone conversation organized by Trump.
Trump added that he believed the crisis could be solved "fairly easily".
Trump also spoke to Qatar's al Thani on Thursday.
Qatar has strongly denied the charges against it, while rejecting a list of 13 demands put forward by the bloc for resuming diplomatic ties.
At Sunday's press conference in Jeddah, al-Jubeir said Riyadh's position vis-à-vis Qatar "will remain the same until Doha meets our demands".
Qatar hosts a huge American air base, home to the headquarters of Centcom - the regional command which leads operations against the Islamic State jihadist group.
Japan's Foreign Minister Taro Kono asked his Qatari counterpart on Saturday for the Middle Eastern country to stop accepting North Korean laborers, in line with a proposed United Nations sanctions resolution calling for a ban on accepting such workers, a Japanese official said.