The two strong-willed leaders have developed a close working relationship since Putin gave his backing to Sisi's presidential run during the latter's visit to Moscow in February.
Russian television showed the former field marshal strolling with Putin through a Black Sea ski resort used during the recent Winter Olympic Games.
"All the people of Egypt are closely watching my visit and expecting a high level of cooperation between our states," Russian state news agencies quoted Sisi as telling Putin.
Sisi also thanked Putin for being the first leader to invite him for a visit outside the Arab world since his swearing in as head of state.
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Russia has jumped at the chance to grab a bigger share of the Egyptian arms market after the United States suspended some of its weapons deliveries last year in the wake of Sisi's crackdown on the former Islamic government.
Cairo hosted the Russian defence and foreign ministers in November -- the first such visit since the Soviet era -- for discussions on an Egyptian arms purchase plan.
The report said Moscow and Cairo had already either "initialled or signed" contracts for the purchase of Mig-29 fighters and Russian attack helicopters as well as coastal defence systems.
"Egypt is most interested in air defence systems," said Moscow's World Arms Trade Analysis Centre chief Igor Korotchenko.
"I think that the signing of actual contracts is just a question of time," the analyst said in a telephone interview. "A political-level agreement has already been reached."
Russian state media said the two sides were expected to kickstart negotiations about establishing a free trade zone between Egypt and a customs union Russia has forged with ex-Soviet Belarus and Kazakhstan.
Moscow in recent decades has played a reduced role in helping resolve the Israeli-Palestinian standoff. The Kremlin has formally backed Gaza mediation efforts currently being conducted in Cairo.