MOSCOW — President Vladimir V. Putin responded within hours Monday to accusations that his government ran a covert doping program for Russian Olympians and other elite athletes, indicating how seriously the Kremlin took the charges.

The government often waits days to react to issues raised abroad, if it responds at all, but international sports competitions in general and the Olympics in particular are important to Mr. Putin.

The president harnessed the success of the 2014 Winter Olympics at the Russian resort of Sochi as proof that he is the leader to bring the nation, as is said here, “off its knees” after the chaotic collapse of the Soviet Union. The Russian haul of 33 medals, seven more than any other country, was offered as the evidence.