The US also has a large military base in Qatar and the Pentagon has voiced support for Qatar's fight against Islamic State (IS) militants in Syria and Iraq.
It was a stark departure from a stern 13-point list of demands issued by the quartet and leaked last week, in which Qatar was apparently told to shut down Al Jazeera, reduce ties with Iran and halt a Turkish military base in the country.
Host of the meeting, Sameh Shoukry noted that Qatar's response was "not serious" and betrayed Qatar's "failure" to realize the gravity of the situation.
He said the demand shows "a lack of respect toward us and Qatar".
Speaking after a meeting with Qatari Foreign Minister Mohammed bin Abdulrahman Al-Thani in Doha on Tuesday, Gabriel praised Doha's "really restrained" reaction to the conflict.
Qatar has countered that the Arab countries want to curb free speech and take over its foreign policy, saying their 13 demands are so harsh they were made to be rejected.
Arab states that have imposed sanctions on Qatar, accusing it of links to terrorism, were due to meet in Cairo on Wednesday to consider Doha's response to a stiff ultimatum, but settlement of the dispute seemed far off.
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Qatar faces further isolation and possible expulsion from the Gulf Cooperation Council (GCC) if its response to a list of demands made almost two weeks ago is not deemed satisfactory.
The Saudi foreign minister said further steps would be taken against Qatar at the appropriate time, and would be in line with global law. "But the Gulf countries consider the Muslim Brotherhood a terrorist group, the United States has not labeled the Muslim Brotherhood a terrorist group thus far".
"Qatar has not taken counter-measures, has not considered how it can attack the other countries in a similar way, economically or politically, but from the first minute has tried to ask for dialogue", Gabriel said.
The Saudi-led group announced no new sanctions but indicated that Qatar could be expelled from the Gulf Cooperation Council.
The decision not to respond immediately with fresh measures may reflect pressure from western capitals to ease the dispute, and the effectiveness of Qatar's campaign to present itself as an innocent victim of an attempt to meddle with its foreign policy, The Guardian comments.
The tone was more balanced than Trump's previous statements, which had offered all-out support for Saudi Arabia and its agenda.