This year's grand prize winners drive off in their new SUV
Sergei Morozov wants couples to take the day off work to have sex. If a baby is born on national day, they will receive cars, TVs or other prizes.
Mr Morozov has declared Wednesday "family contact day" as part of efforts to fight Russia's demographic crisis.
The population has sharply declined since the Soviet Union collapsed.
This is the third year that Ulyanovsk, in central Russia, is offering prizes for babies born on 12 June.
This year, a couple won the grand prize of a sports utility vehicle (SUV).
The initiative seems to be paying off, as the region's birth rate has risen by 4.5% over the last year.
"If there's a good, healthy atmosphere at home within the family, if the husband and wife both love each other and their child, they will be in good spirits... so there'll be a healthy atmosphere throughout the country," Mr Morozov told the Associated Press news agency.
Demographers estimate that Russia could lose 40 million people - almost a third of its current population - by the middle of the century.
A combination of falling birth rates, emigration and an ailing healthcare system has led to the decline.
President Vladimir Putin has introduced a scheme to encourage more children.Women who have a second or third child are eligible to receive $9,000, which can be used to pay for education or home purchases.