The plan, proposed by the pro-Kremlin United Russia party, would require the turnout of a majority of eligible voters to validate regional elections, Veshnyakov said.
If an election is deemed invalid, the president would have the power to appoint a temporary governor who could serve up to two years, the CEC chief said Tuesday after meeting with United Russia members.
The Constitution currently prohibits the president from appointing governors.
Veshnyakov said he backed requiring a candidate to land a majority of votes cast to be declared the winner. United Russia's original proposal called for a majority of all registered voters.
If no candidate wins a majority or if turnout fails to surpass 50 percent, a region would have to hold a second round of voting, Veshnyakov said.
He said the proposed legislation was still under development but could be enacted by the end of the year.
Local election laws are now set by regional authorities. Most candidates need only a simple majority of votes cast, provided that the turnout is above a region's required minimum.
United Russia officials last month said their proposed bill would level the political playing field and encourage voters, but critics said the initiative would do just the opposite and represented another attempt by the Kremlin to bring politics under its control.
A requirement stating that at least 50 percent of all eligible voters must show up at polling stations to make gubernatorial elections valid would be difficult to meet. Of 15 gubernatorial elections held last year, nine saw less than a 50 percent turnout.
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