By Valerie Volcovici

WASHINGTON (Reuters) - Virginia's governor issued an order on Tuesday to lay the groundwork for a cap-and-trade system to cut greenhouse gas emissions from power plants, saying it would "fill the void" left by the Trump administration which has been rolling back federal climate rules.

Democratic Governor Terry McAuliffe signed Executive Directive 11 instructing Virginia's environmental regulators to craft rules targeting power sector carbon emissions by Dec. 31.

McAuliffe specifically asked regulators to propose a rule for the state air pollution control board that would enable Virginia to participate in a multi-state carbon permit trading program such as the Regional Greenhouse Gas Initiative for northeastern states.

"As the federal government abdicates its role on this important issue, it is critical for states to fill the void. Beginning today, Virginia will lead the way to cut carbon...,” McAuliffe said in a statement.

The main federal environmental regulator, the Environmental Protection Agency, has been actively rolling back Obama administration rules aimed at combating climate change, including the Clean Power Plan that aimed to slash carbon emissions from power plants by 32 percent below 2005 levels by 2030.

McAuliffe said Virginia was especially sensitive to the impact of climate change and dealt with the frequent threat of storm surges and flooding.

Environmental groups praised the governor's order, which they said was an antidote to the Trump administration's efforts to roll back Obama-era environmental laws.

"In the face of dangerous rollbacks of clean air protections from the Trump Administration, Governor McAuliffe’s directive is one more example of state leaders moving forward," said Gene Karpinski, president of the League of Conservation Voters.

Republicans in Virginia called McAuliffe's move a costly policy that would raise electricity prices for Virginians.

"Governor McAuliffe's executive order is the worst kind of virtue signaling," said John Whitbeck, chairman of Virginia's Republican party.

(Reporting by Valerie Volcovici; Editing by Dan Grebler and Andrew Hay)