However, Saudi Arabia then accused Qatar of distorting facts about the call, and said it was ending talks.
The four countries say Qatar supports terrorism - something Doha denies.
The row led to all four Arab nations cutting ties with Qatar on 5 June - Saudi Arabia closed its land border with Qatar, while all four countries cut air and sea links with the country.
Friday's phone call, which came after US President Donald Trump spoke separately with both sides, had initially been seen as a possible breakthrough in the crisis.
The call was the first formal contact between Riyadh and Doha since the crisis began.
State media on both sides reported that Qatar's Emir Sheikh Tamim bin Hamad al-Thani and Saudi Crown Prince Mohammed bin Salman had discussed the need for dialogue to resolve the crisis.
More about: #Qatar
