Lawmakers are demanding changes in how the government tracks terrorists online, aiming to bring the methods in line with those for catching child predators in the wake of the Paris and San Bernardino attacks.

A Senate bill introduced this month by Sen. Dianne Feinstein, D-Calif., and Sen. Richard Burr, R-N.C. -- which uses anti-child pornography laws as a model -- would require technology companies to report terrorist activity to law enforcement.

“We’re in a new age where terrorist groups like ISIL are using social media to reinvent how they recruit and plot attacks,” Feinstein said in a statement. “That information can be the key to identifying and stopping terrorist recruitment or a terrorist attack, but we need help from technology companies.”

The Islamic State has shown social media savvy, using tools like Facebook and Twitter to spread its message and recruit, despite frequently having accounts shut down. The pressure in the U.S. to crack down has grown amid speculation about San Bernardino shooters Tashfeen Malik and Syed Rizwan Farook's social media comments -- though FBI Director James Comey says their discussions were not public.

The Feinstein-Burr bill is based on a law already in existence that requires companies to report child pornography.

The bill came under fire from Democrats who claim it would incentivize companies not to look for terrorist postings.

“It would create a perverse incentive for companies to avoid looking for terrorist content on their own networks, because if they saw something and failed to report it they would be breaking the law, but if they stuck their heads in the sand and avoided looking for terrorist content they would be absolved of responsibility,” Sen. Ron Wyden, D-Ore., said in a statement.

Some Republicans also were critical of the bill for putting too much emphasis on the responsibility of the private sector.

"The burden should be a shared burden but the primary responsibility should be on the government because they are ultimately responsible for keeping America safe, not commercial entities," Bradley Blakeman, former assistant to President George W. Bush, told FoxNews.com LIVE.

The House passed legislation on a bipartisan vote last week that requires President Obama to produce a strategy to combat terrorists online, relating specifically to social media.

Social media companies have responded that they are already doing enough when it comes to reporting online terrorism.

"Violent threats and the promotion of terrorism deserve no place on Twitter and our rules make that clear,” a spokesperson for Twitter told FoxNews.com. “We have teams around the world actively investigating reports of rule violations, and they work with law enforcement entities around the world when appropriate."

The company also said their rules ban users from making violent or terroristic threats, and noted they had 3,436 information requests from U.S. law enforcement in the first half of 2015.

That hasn’t stopped the growing calls for change from Washington D.C., including from presidential candidates.

Republican Carly Fiorina told Fox News’ Greta Van Susteren that she would call private sector companies to make sure they were enlisted in the fight against terrorism.

“I would make several calls. I would make calls to the heads of every social media company, I would make calls to the heads of Google,” Fiorina said.

“We know where these websites are and there are absolutely ways in both hardware and software to understand who is traveling to these websites. Let’s use that capability instead of getting hung up in a bunch of high-bound bureaucratic procedures, including the fact that many of these departments are clearly being told, 'Oh, don’t do that it’s not politically correct, you might harm someone’s civil liberties.' We’re at war,” Fiorina said.

Some tech experts disagreed with the idea that social media companies are dragging their feet, or that there is a difference in the way terrorists are treated compared with child pornographers.

“There is no discrepancy between how laws and social media companies treat child pornographers and terrorists,” Pierluigi Paganini, founder of the blog “Security Affairs,” said. “Clearly the recent climate of tension has shifted the focus of IT companies on terrorism-related abuses (i.e. sharing of propaganda content), but it does not mean that a terrorist is treated differently from a pedophile.”

The White House has said it is reaching out to the tech industry and is hopeful companies would play an “active role” and work with the government to stop terrorists from finding an online safe haven.

“Now, this raises a bunch of thorny questions,” White House Press Secretary Josh Earnest said earlier this month. “And we’re going to resist the urge to go and trample a bunch of civil liberties here, but there are steps that we believe we can work through with the technology companies to take some common-sense measures that would enhance public safety.”