Scuffles have been reported at one of Moscow's largest airports as disruption caused by bad weather continues for another day.
At Sheremetyevo, north of the capital, stranded passengers were said to have beaten up staff from the Russian airline, Aeroflot.
Freezing rain at the weekend led to the cancellation of hundreds of flights at Sheremetyevo and Domodedovo airports.
President Medvedev has ordered an investigation into the delays.
Prosecutors will also look at whether the airports and the companies linked with them have offered passengers all the services they are legally entitled to.
Passengers at Sheremetyevo attacked a number of Aeroflot employees, including women, the Russian news agency RIA-Novosti reported, quoting a source at the airline.
Police from the Omon special force were deployed at both airports following incidents on Monday.
A group of angry passengers stormed passport control at Domodedevo, while a YouTube video showed hundreds of people sitting on the floor in the security area at Sheremetyevo, chanting "Shame!"
The freezing rain resulted in a complete power shutdown over the weekend at Domodedovo - caused by tree branches touching power lines loaded down with ice.
Reports said the authorities had failed to provide food and basic facilities to passengers, who had to wait for their flights in the dark.
Russian Transport Minister Igor Levitin has strongly criticised the way airport officials handled the power cuts.
"Here is a question for the airport's management - why did they keep receiving passengers?" Mr Levitin said, according to the Itar-Tass news agency.
"After the lights went out, they should have shut!"
On Tuesday a passenger at Domodedovo told Interfax news agency there were still problems with power, ventilation and water supplies in airport toilets.
"People are on the verge of a nervous breakdown," she said.
Travellers were reported to be camped on the floor waiting for information on their flights. Many had lost items of luggage.
A limited number of aircraft began leaving Domodedovo on Monday, but officials say it will take another two or three days for the situation to return to normal.