"We are greatly concerned about the media reports that a US adoptive father shot two adopted children from Russia. Now we are checking the information," Konstantin Dolgov posted to Twitter.
The Russian Federation Council, or the upper house of the country's parliament, has also said it is monitoring the developments of the investigation on the shooting.
Since January 2013, US citizens are banned from the adoption of Russian children under the law, which also marked the withdrawal of Moscow from a US-Russian agreement on cooperation in child adoptions concluded in 2011.
The measure is also known as the Dima Yakovlev Law, named after a Russian toddler who died in the United States in 2008 after being locked in a car by his adoptive father, a US citizen.