Saudi Arabia, the United Arab Emirates (UAE) and Bahrain agreed on Sunday to return their ambassadors to Doha after resolving their row with Qatar.
In a statement on Wednesday, Saudi King Abdullah appealed to the leadership and people of Egypt to "work with us for the success of this step in the march of Arab solidarity", the Saudi Press Agency reported.
Three hours later, the office of Egyptian President Abdel Fattah al-Sisi issued a statement calling the king’s appeal "a big step towards Arab solidarity".
"We look together to a new era that turns the page on the disputes of the past," it said.
Saudi Arabia has strongly supported Sisi and contributed billions of dollars of aid to Egypt since he ousted elected President Mohamed Mursi of the Brotherhood last year.
The Egyptian statement did not mention Qatar by name. Relations between Cairo and Doha have deteriorated since the army removed Mursi and the Brotherhood from power following mass protests against his rule.
Egypt’s ambassador to Qatar was recalled to Cairo earlier this year over political tension between the two states.
Like Egypt, the UAE and Saudi Arabia have listed the Brotherhood as a terrorist organisation and see political Islam as a challenge to their own systems of rule.
Qatar is seen to have been supportive of the Brotherhood in Egypt and the UAE, and more recently in Libya. It had given sanctuary to some Brotherhood members but in September asked seven senior figures from the group to leave the country following months of pressure from its neighbours.
Riyadh and Abu Dhabi also see the Doha-based Al Jazeera news network as being a Brotherhood mouthpiece, which Qatar denies.
Sisi issued a decree last week allowing him to repatriate foreign prisoners in Egypt, which could enable him to release at least one of three Al Jazeera journalists currently serving a seven-year jail term for spreading lies.