The Russians have assisted the Northern Alliance
The delegation is the first from a foreign country since the former opposition took Kabul and large parts of the country from the Taleban last week.
The move is being seen as a clear indication of Moscow's intention to play a major role in establishing a future government in Afghanistan.
Iran, which also supports the Northern Alliance, announced on Saturday that it intends to be the first country to reopen its embassy in Kabul.
The Russian team is due to meet ousted Afghan President Burhanuddin Rabbani, who heads one of the main Northern Alliance factions.
The UN has recognised him as the country's president ever since he was ousted by the Taleban five years ago.
But it now does not want him to assume the same role, and is working to set up a broad-based government in Afghanistan.
Stable regime
Both Russia and Iran are known to support his taking a leading role in any new administration.
Moscow wants a stable, non-extremist government in Kabul, with which it could set up diplomatic relations.
Russian Defence Minister Sergei Ivanov has described the Northern Alliance as the legitimate government of Afghanistan.
But central Kabul is controlled by just one part of the Northern Alliance - Mr Rabbani's Jamiat-e-Islami - and other parties in the Alliance want to share in the power.
Ten years after the break-up of the Soviet Union, the former Soviet Central Asian states bordering on Afghanistan - Tajikistan, Uzbekistan and Turkmenistan - continue to be seen by Moscow as important strategic territory.
The last Soviet troops pulled out of Afghanistan in 1989 after a decade of fighting Islamic guerrillas opposed to the then Moscow-backed regime in Kabul.
But Russia has admitted officially to arming the Northern Alliance in Afghanistan for years.