He argued that the government has worked with the private sector for decades to protect the physical security of critical assets "from airports and seaports to national broadcast systems and nuclear power plants."
"There is no reason we cannot also cooperate to protect the cyber systems of critical infrastructure on which our economic well-being, national security and daily lives depend," he wrote.
But Brennan said the president lacks the legal authority to grant legal protection to companies that choose to share cyber threat information with one another and with the government.
Information-sharing was a core piece of the Senate cybersecurity bill and the focus of the House GOP bill on the issue.
Brennan urged Congress to keep working on comprehensive legislation, including protections for information sharing.
"Comprehensive legislation remains essential to improve the cybersecurity of the nation's core critical infrastructure, to facilitate cyber information sharing between the government and the private sector, to strengthen and clarify the existing patchwork of authorities regarding federal network security, and to protect the privacy and civil liberties of American people," he wrote.
In a statement, Rockefeller agreed that Congress should not give up on passing a cybersecurity bill.
"The cyber legislation that was just debated on the Senate floor was a strong bill but Senate Republicans stood with beltway lobbyists over our military and national security officials' professional advice, and filibustered the Cybersecurity Act," said Rockefeller, who co-sponsored the bill. "The White House knows how serious the cyber threats facing our country are and I am grateful that they are working to take appropriate action, though we still should pass comprehensive reforms soon.”
In an interview on MSNBC on Monday, Sen. Kay Bailey Hutchison (R-Texas) argued that an executive order would impose burdensome regulations on businesses.
"What the president is contemplating doing is a heavy regulatory environment where he is going to tell the companies that they consider critical infrastructure to go through the lens of the Department of Homeland Security," Hutchison said.