By Patricia Zengerle

WASHINGTON (Reuters) - American intelligence agencies are concerned about reports that foreign governments may be attempting to undermine the Nov. 8 U.S. elections through cyber attacks, Admiral Mike Rogers, the director of the National Security Agency, said on Tuesday.

"We continue to be actively concerned," Rogers told a Senate hearing, responding to a question from Senator John McCain, chairman of the Senate Armed Services Committee.

Marcel Lettre, Under Secretary of Defense for Intelligence, testified that the government is taking any such activities "quite seriously" and said an "aggressive investigation" is under way.

McCain noted that one of the two states in which media reports said there was evidence of attempted Russian hacking was his home state, Arizona.

Some analysts have said Arizona, which recently has been reliably Republican in presidential elections, could be tilting more toward the Democratic nominee, Hillary Clinton, this year. McCain, a Republican, himself is in a tougher than usual re-election fight.

Rogers said he could not provide specifics about spy agencies' current assessment of the alleged hacking in a public setting. But he added, "I will say this, that it continues to be an issue of great focus ... for the foreign intelligence community, attempting to generate insights into what foreign nations are doing in this area."

Under further questioning, Rogers declined to characterize the activity as by a foreign nation-state.

Lettre said the government would adopt a policy for dealing with any such activity once it had the results of the investigation.

"The FBI and the Department of Homeland Security has an aggressive investigation underway," Lettre said.

U.S. security officials have said that, starting last year, hackers infiltrated computers of the Democratic National Committee, Clinton's presidential campaign and her party's congressional fundraising committee.

U.S. officials said they have concluded that Russia or its proxies were responsible, leading to calls by some Democrats and cyber security officials for the Obama administration to blame Russia publicly.

Kremlin officials have dismissed the allegations as absurd, but there is anxiety in Washington over the possibility that a foreign power might be using hacked information to meddle in the November elections.

(Reporting by Patricia Zengerle; Editing by Jonathan Oatis)