Putin ordered Sports Minister Vitaly Mutko and "all colleagues connected with sport" to pay close attention to the doping allegations and for an internal investigation to be conducted - one that guaranteed full cooperation with international anti-doping bodies.
"The struggle with doping in sports, unfortunately, remains a pressing issue and it requires unending attention," he said.
Putin is up against a Friday deadline for track's governing body to decide on whether to suspend Russia - a first step toward excluding its athletes from next year's Olympic - following WADA's report.
Earlier, Mutko said the country was ready to allow a foreigner to take charge of its anti-doping lab.
Grigory Rodchenkov resigned yesterday as director of Russia's anti-doping laboratory, a day after he was accused of concealing positive doping tests, extorting money from athletes and destroying 1417 samples.
The lab - which handled doping tests for last year's Winter Olympics - has stopped work after Wada stripped its accreditation.
In comments reported by Russian agency R-Sport, Mutko said Russia was ready "to put a foreign specialist in charge of the laboratory, if that's what's needed".
The governing body of swimming said today it is moving its doping test samples taken at the world championships in Russia to the WADA-accredited lab in Barcelona.
FINA said in a statement that it "expresses its deep concern" over the publication of the WADA-commissioned report "and its impact in worldwide sport in general".
IOC president Thomas Bach said he expected the IAAF to take "necessary measures" against the Russian track and field federation on Friday.
Russia could be suspended from the sport - nine months before next year's Olympics - when IAAF president Sebastian Coe convenes a meeting of his ruling council.
Bach told reporters in Lausanne, Switzerland, that "the IAAF has informed us they will take the necessary measures". Bach said he expects the IAAF decisions will "protect clean athletes".
Russian track federation vice president Tatyana Lebedeva, a former Olympic long jump champion, said the organisation has carried out enough reforms to deserve a place at next year's Olympics despite the doping scandal.
Lebedeva told The Associated Press "our federation has done everything possible that was in its power" to reform over the last year, since a German documentary about systematic doping in Russia aired.
- Agencies