White House press secretary Josh Earnest speaks to the media during the daily briefing in the Brady Press Briefing Room of the White House, Tuesday, July 8, 2014.

Media Organizations Want More Access

White House claims it is most transparent in history.

White House press secretary Josh Earnest speaks to the media during the daily briefing in the Brady Press Briefing Room of the White House, Tuesday, July 8, 2014.

White House press secretary Josh Earnest speaks to the media. Earnest said Sunday the Obama administration is "absolutely" the most transparent in history.

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The battle between the press corps and the White House is heating up again.

Even though correspondents hoped for improved relations when the genial Josh Earnest replaced the often combative Jay Carney as White House press secretary last month, things haven't changed enough to satisfy the media. Last week, more than 40 news organizations urged President Barack Obama and other federal officials to be more transparent and to "stop the spin and let the sunshine in." The signees of the letter making those points included the Society of Professional Journalists, the Poynter Institute and the National Press Foundation.

[READ: Jay Carney and the 'Theatrical' Press]

But Earnest told CNN Sunday that the Obama administration is "absolutely" the most transparent in history. Yet he added he expects the media to continue pushing for more information and access.

"If there's ever a day when the White House press corps sits back and says, 'You know, we're getting all the information that we need from the White House press office,' then everybody in the White House press corps would not be doing their jobs, right," Earnest said.

Among the complaints of news media representatives are that the White House has prosecuted whistleblowers, and is forcing the media to deal increasingly with public relations specialists in government and not the actual policymakers. This emphasizes spin and shortchanges the public, media representatives say. Administration officials, including Obama, also are faulted for saying Americans could keep their existing health insurance if desired, which didn't turn out to be true under Obama's legislative overhaul of health care.

On the positive side, Earnest said the administration has routinely posted White House guest lists on the Internet, and reporters now have some access to the president at fundraising events held in private homes.