The conditions include severing ties with the Muslim Brotherhood, scaling back relations with Iran, Saudi Arabia's rival for regional hegemony; shutting the government-funded Al Jazeera television station, which has been critical of other autocratic governments in the region; and end Turkey's military presence in Qatar.
"Measures agreed with the United States on combatting counter-terrorism financing and also with Germany as an auditor are strong components of a positive broader settlement that allows both sides a measure of face saving", said Andrew Bowen, a Gulf scholar with the American Enterprise Institute who has met recently with officials from both sides of the dispute.
The foreign affairs think tank called for a public inquiry into the role of Saudi Arabia and other Gulf nations.
The top diplomats met in Cairo, a day after they received Qatar's response to a list of 13 demands that the country must meet or else face continued sanctions by its neighbours.
Al Jazeera's Senior Political Analyst Marwan Bishara says the four Arab countries that have cut ties with Qatar have limited choices when it comes to increasing pressure on the emirate.
Despite the optimism from those in the Europe and the USA, officials from the countries that accuse Doha of financing and promoting extremism say that Qatar's rejection of their demands means additional measures are now being discussed.
The Saudi foreign minister said further steps would be taken against Qatar at the appropriate time, and would be in line with global law.
On Tuesday, German Foreign Minister Sigmar Gabriel visited officials in both the United Arab Emirates and Qatar.
Egyptian President Abdel Fattah al-Sisi spoke with US President Donald Trump by telephone about Qatar, Sisi's office said on Wednesday.
Saudi Arabia, Bahrain, UAE and non-GCC member, Egypt, accuse Qatar of supporting terrorism and backing a number of groups including the Muslim Brotherhood. "We are states of sovereignty, and we have the right to take any measures in line with worldwide law", the Saudi Foreign Minister elaborated. He also said that the current embargo will remain in place unless Qatar revises policies.
In addition, Doha excludes the possibility of closing the Turkish military base, arguing that the Charter of Gulf Cooperation Council (GCCC) does not prohibit such cooperation with other countries.
The White House said Trump reiterated the need for all countries "to stop terrorist financing and discredit extremist ideology".