Egyptian Defence Minister Abdel-Fattah El-Sisi and Foreign Minister Nabil Fahmy discussed military cooperation with Russian ministers in Moscow on Wednesday.
Anonymous Egyptian military sources have told Al-Ahram Arabic news website that El-Sisi is in Moscow to finalise a weapons deal made when Russian Defence Minister Sergei Shoygu visited Cairo in November.
Fahmy said the talks reflect a serious desire to increase regional and international dialogue, Russia Today reported.
He said talks with Russian Foreign Minister Sergei Lavrov discussed Russian support for bringing stability to the Middle East and increasing unity among the countries of the region.
But Fahmy emphasised Egypt was not replacing one international partner with another - a veiled reference to the United States.
"No one wants to rewrite history, Egypt does not want to replace one international partner with another," he told Al-Ahram Arabic news website's correspondent in Moscow, adding that there were common interests between the countries both regionally and globally.
"These 2+2 talks [between defence and foreign ministers] reflect how important Egypt is for Russia and how excellent relations are between us," he added.
Fahmy said he would discuss the Ethiopian Renaissance dam with his Russian counterparts but would stress the importance of the issue without criticising Ethiopia.
He also hinted that further talks would include discussions about counter-terrorism cooperation, without giving further details.
Russian Foreign Minister Sergei Lavrov said Wednesday's talks were important "at such a point in time" and emphasised Russia's desire to "enhance bilateral relations that have continued alongside decades of mutual respect and cooperation."
The talks are encompassing technical, humanitarian, economic and military issues, Lavrov added.
Shoygu said he was "closely following" political developments in Egypt.
"We are concerned about creating a strong and stable Egyptian state."
Shoygu congratulated El-Sisi on his recent promotion to the rank of field marshal, which showed Egypt's "appreciation for his role in maintaining the country's peace and security."
Russia's top military official said he supported Egypt's fight against terrorism and called for greater cooperation in military affairs.
Terrorism is one of many problems facing Egypt during this "tough period," Shoygu added.
Energy, economic cooperation, tourism and fighting terrorism will be discussed at further meetings, Russia Today reported.
Egypt had close ties with Russia until several years before president Anwar Sadat made peace with Israel in 1979. Egypt then became a close ally of the United States, which has delivered $1.3 billion in annual military aid in the subsequent decades.
El-Sisi congratulated Russia for organsing the Winter Olympics in Sochi.
The talks will continue on Thursday.