It was the third attack on the Black Sea port in less than two weeks. Ukraine's military confirmed it had carried out the strike, the latest in a series designed to disrupt Russia's oil industry and slash revenue that helps Moscow fund the war in Ukraine.
Putin, in comments broadcast on Russian television, said: "Drone strikes against civilian infrastructure are becoming more frequent.
"The latest example is the strikes against energy facilities in Tuapse, which could potentially cause serious environmental consequences," he said.
Putin said regional Governor Veniamin Kondratyev had reported there were no major threats.
"It seems there are no serious dangers, and people are managing to deal with the challenges they face on the ground," he added.
Emergencies Minister Alexander Kurenkov, dispatched by Putin to the region, was quoted by Russian media as describing the situation as "complicated but controllable."
Kurenkov said the flow of oil products into the Black Sea had been stopped and booms would ensure the spills did not spread.
Kondratyev said firefighting teams were working to bring the blaze under control and an additional 300-member emergency crew would arrive on Wednesday.
The Kremlin accused Ukraine of exacerbating a global oil shortage by targeting storage facilities containing oil intended for export.
The Ukrainian foreign ministry did not immediately respond to a request for comment on Moscow's accusations.
Images on social media showed dense black smoke rising from the direction of the Tuapse refinery.
Following an attack on April 20, black rain fell on the Black Sea port town and a beach resort, leaving an oily residue.
The refinery halted production on April 16 because of drone damage to the port that made it impossible to ship its production, industry sources told Reuters. At least three people have been killed in the strikes, according to officials, and one of them led to an oil spill at sea.
The head of the Tuapse district, Sergei Boyko, ordered residents near the refinery to evacuate to a school.
Kremlin spokesman Dmitry Peskov said authorities were "working intensively" to combat Ukrainian drone strikes.
Ukraine has stepped up its attacks on Russian energy targets since March, with US-brokered peace talks on pause and Washington mainly focusing on the Iran war.
The Tuapse refinery has annual production capacity of about 12 million metric tons, or 240,000 barrels per day, turning out naphtha, diesel, fuel oil and vacuum gasoil.
Separately, President Volodymyr Zelenskiy said the Ukraine is preparing to export weapons as it is producing more than its armed forces require.
"In some production areas, we currently have up to 50 per cent surplus capacity," he said during his nightly address.
"The export of Ukrainian weapons will become a reality. The Ukrainian military will always have the right to priority and sufficient supply - they will take what is needed, and the volume beyond that will go to export."
Zelensky said Ukraine was already working with countries in the Middle East, Europe and the Caucasus under a special co-operation format known as "drone deals."
"A proposal is also on the table for our American partners," he added.
with DPA
