Friedman said she's open to working with Newsom to make sure he has the authority to issue a moratorium on new fracking permits.
"We look forward to having a clean economy, using renewable sources of fuel. We have to start setting ourselves seriously on the road to accomplishing that. If the governor thinks he needs the Legislature's help ... to make that vision happen, I stand willing and able to do that," she said.
Stern said the governor may already have the authority to issue a moratorium.
"He's got a lot on his plate. Now this one has got to move to the top of the agenda. It's an urgent situation," said Stern.
Stern was an aide to then-state Sen. Fran Pavley when she wrote SB 4, state legislation that led to new rules regulating hydraulic fracturing in California.
The Western States Petroleum Association, which represents the region's oil industry, told KQED that a halt in new fracking operations would hurt the economy.
"Shutting down oil and gas production would increase dependence on foreign oil from the Middle East, eliminate hundreds of thousands of good-paying careers — including opportunities for blue collar and labor workers — and make energy less affordable for middle and working class Californians," Catherine Reheis-Boyd, the association's president, said in an emailed statement.
"Historically, our industry has shown a willingness to collaboratively work with regulators and elected officials toward landmark environmental legislation like the Cap-and-Trade program and the (SB4), and we'll continue to work together to drive the most immediate improvements in carbon reductions, economic security, and reliable access to energy for all," Reheis-Boyd said.
Stanford's Sivas said DOGGR has the power currently to stop issuing fracking permits.
"In my view, it could also issue a broader, sweeping set of regulations," she said. "The agency and the governor could say, 'We've studied this and this is not a good way for California to go forward, and we're just not going to do fracking permits anymore.' "