"Due to the fact that unknown persons had accessed the ramp, the decision was made to temporarily shut the airport for inbound and outbound flights," the agency said in a statement.
The airport, servicing the capital of the Muslim-majority Dagestan Republic, will remain provisionally closed for inbound flights until 3 a.m. (00:00 GMT) on November 6, Rosaviatsiya added later. Planes that were due to land at the airport were diverted to alternate airfields.
Videos circulating on social media showed dozens of people storming the ramp after a Red Wings passenger plane from Israel’s Tel Aviv landed at the airport.
The Russian Interior Ministry's regional office said a criminal probe had been launched into the incident on accusations of rioting. Those inciting riots and inciting ethnic hatred will be held criminally liable, the ministry added.
The Dagestan authorities said they would limit traffic on the highway leading to the airport.
Police promptly took the situation under control, the Dagestan government said on social media shortly after the security breach was reported. All trespassers were removed from the runway.
The airport storming comes amid unauthorized pro-Palestinian protests that broke out across Dagestan over the weekend after Israel intensified bombardments of the Gaza Strip.
Russia's chief rabbi, Berl Lazar, called on all confessions to resist attempts to sow discord among the peoples of Russia.
The Israeli Prime Minister's Office, the Ministry of Foreign Affairs and the National Security Council said they were monitoring events unfolding in Dagestan and urged the Russian authorities to guarantee security of Israeli citizens and Jews.
"Israel expects the Russian legal authorities to safeguard the well-being of all Israeli citizens and Jews wherever they are and to take strong action against the rioters and against the wild incitement being directed against Jews and Israelis," they said in a joint statement.
Israeli Ambassador to Russia Alex Ben Zvi is working with the Russian authorities to secure the well-being of Jews and Israelis at the site, they added.
The Dagestan government has called an emergency meeting in response to the airport storming and the broader "socio-political situation in Dagestan." It will be chaired by Governor Sergei Melikov.
As a result of the unrest at the airport, more than 20 people received injuries, including law enforcement officers, the regional department of the Health Ministry said later.
"Medical personnel of the republican hospitals are providing assistance to 10 injured people … Both police officers and civilians received moderate and severe injuries. Two people are in extremely serious condition," the department said on Telegram.
In addition, over 10 people with minor injuries sought outpatient medical care, the statement read.