The October 10 to 12 event, the first on Russian soil, will take place at the Sochi Olympic Park in the Black Sea resort, where athletes this week began competing in the Paralympic Games.
Putin, under international pressure over the situation in neighboring Ukraine, where thousands of pro-Russia troops have fanned out across the Crimean peninsula, told Ecclestone the race would be a good use of the Olympic venue.
"It allows us to use the infrastructure more effectively once these big competitions come to an end," he said.
Putin acknowledged that there remained work to be done ahead of the race, which was added to the calendar for this season as part of a revamp of the line-up.
But, he said, difficulties had been of a practical, rather than a conceptual nature.
"We will overcome them. It is very pleasing for me that the project is going to be a bright, beautiful addition to what was done in the preparations for the Olympic Games and the Paralympic Games," he said.
The Russian president did not give details of the problems, but reports have suggested a large number of stray dogs is a worry for organizers, while some of the facilities remain unfinished.
"We have been working on the project to bring Formula One to Sochi for a long time and it is moving to its full conclusion," he said.
The 19 races of the 2014 Formula One season begin next weekend in Melbourne.