The DHS alerts were far more specific than the ICS-CERT advisory and contained details like file names, IP addresses and other markers that a company could use to see if it was breached, The Monitor said in its report.

Interestingly, one of the alerts asked companies that believed they had been breached, not to do anything to stop the malicious activity on their networks The Monitor said, quoting an individual who claimed to have seen the alert.

The goal apparently is to gather as much information on the attacks as possible without tipping the attackers that they had been discovered, the report said.

Patrick Miller, principal investigator of the National Electric Sector Cybersecurity Organization, said that the wording in the alerts suggest that at least some organizations may have been breached. "We haven't seen any raw breach data, but it is implied based on what we have noticed [in the alerts]," he said. "We do have indicators that the threat is active."

News of the ongoing so-called attempts is sure to focus attention on the ability of U.S. critical infrastructure organizations to withstand targeted and persistent attacks.