Going through the list of members of the 1917 Council of People's Commissars (SovNarKom), which is available online in both Russian and English, I found only three whose names or biographical information provide any reason to believe that they were Jews: Isaac Steinberg, Boris Kamkov (Katz) and Alexander Shotman. Trotsky was not one of the 17 members of the SovNarKom. I wonder where Mr. Putin got his information.
Opposition leader Isaac Herzog to speak at anti-violence rally in Tel Aviv on Sat. night (Haaretz)
from the article: Putin: First Soviet government was mostly Jewish