(Reuters) - Eight top Republicans introduced a cybersecurity bill on Thursday aimed at stopping an overarching, bipartisan measure proposed earlier this month in order to better protect critical infrastructure.

The measure, introduced by the top Republicans on eight committees, would require federal contractors to inform the government about cyber threats and make it easier for government regulators and corporations to communicate about threats.

We believe that ensuring our nation's cybersecurity is critical. We have a bill that would do plenty to meet current challenges, said Senator John McCain in introducing the bill.

McCain, a critic of a measure supported by Senate Majority Leader Harry Reid, argued that the Republican-backed legislation was better because it included very little new regulation.

The Arizona Republican has also been critical of proposals to have the Department of Homeland Security take a leading role in pushing better cyber security practices on sometimes reluctant industries.

Senator Saxby Chambliss, a co-sponsor of the McCain measure, agreed, saying: More government is seldom a solution to any problem.

The Senate is also considering a rival bill Reid has said will be brought quickly to the Senate floor.

That bill is aimed at requiring upgrades in security for critical national infrastructure, which some cyber experts argue is needed to prevent a catastrophic attack on the nation's water supply, electric grid, financial networks and transportation infrastructure.

The McCain bill does not include this requirement.

The Reid-backed bill's sponsors include Senators John Rockefeller and Dianne Feinstein, both Democrats; Susan Collins, a Republican, and Joseph Lieberman, an independent.

There has been widespread and growing concern about incursions into U.S. networks by hackers looking to steal everything from state secrets to credit card numbers.

Victims have included defense contractors like Lockheed Martin Corp, web search leader Google Inc, Citigroup bank and exchange operator Nasdaq OMX.

Politicians have not been immune. In 2008, hackers targeted both President Barack Obama and McCain's presidential campaigns.

Reid and the four lawmakers who proposed the broader bill said they viewed the McCain legislation positively.

Reid said in a statement that the McCain measure highlighted areas of agreement. Both measures discuss the need for better information sharing mechanisms. I look forward to a debate on the Senate floor that will ensure this bill and other proposals get a fair hearing, and which will allow thorough consideration of amendments to improve the legislation, Reid said.

The White House is eager to see cybersecurity legislation, but Howard Schmidt, the White House cybersecurity policy coordinator, said that the federal government could do more even without legislation. As one example, the Department of Energy could push harder to prompt electric utilities to ward off hacking intrusions.

The U.S. House of Representatives is considering legislation that overlaps with the Senate measures on some points.

For example, the House's Permanent Select Committee on Intelligence approved a bill in December that would expand a pilot Pentagon program for sharing classified and sensitive threat information with defense contractors and their Internet service providers.

USTelecom, a broadband association, said it supported the McCain measure because it would effectively protect against cybersecurity threats, especially by improving information-sharing.

We can support the bill introduced today because it pursues those objectives without creating new bureaucracies or regulatory mandates that would erode, rather than enhance, the ability of network providers to provide nimble and effective responses to cyber threats, said USTelecom President Walter McCormick.