Ties between Cairo and Doha deteriorated after then army chief Sisi ousted Mohamed Morsi, whose Muslim Brotherhood movement was backed by Qatar.
Since Morsi's ouster in July last year, a crackdown overseen by Sisi against the Brotherhood has left hundreds dead.
Qatar repeatedly denounced Sisi's ouster of Morsi and it still provides shelter for some Brotherhood leaders who fled Egypt.
The crackdown led to a months-long diplomatic spat pitting Qatar against Saudi Arabia, the United Arab Emirates (UAE) and Bahrain, which all supported the ouster of Morsi.
But at a reconciliation summit in November hosted by Riyadh, Qatar joined its Gulf neighbours in supporting Egypt under Sisi.
"Egypt looks forward to a new era that ends past disagreements," Sisi's office said after he met with Sheikh Mohamed bin Abdel Rahman Al-Thani, a special envoy of Qatar's emir, Sheikh Tamim bin Hamad Al-Thani.
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Doha-based Al-Jazeera television has repeatedly condemned Morsi's ouster, while Egyptian media have slammed Qatari authorities for backing the Brotherhood.
Egyptian authorities have jailed three Al-Jazeera reporters, accusing them of biased reporting and aiding the Muslim Brotherhood.
The Riyadh summit came amid security fears over the rise of the Islamic State jihadist group in Syria and Iraq.
Bahrain, Kuwait, Qatar, Saudi Arabia and the UAE have all joined US-led air strikes against the IS in Syria.
Sisi's meeting with the Qatari envoy was his first with a Doha representative since becoming president in June.
The Qatari envoy was accompanied by a special representative of Saudi King Abdullah.