John F. Kerry’s credibility took on more water on the second day of his Nantucket vacation flap, as the State Department backed off its initial denial the embattled secretary of state was yachting during the Egyptian military coup — and President Obama tweeted a photo of himself kayaking in a hat, sunglasses and polo shirt.

The Herald reported yesterday that Kerry spent the Fourth of July cavorting on his island getaway even as chaos from the military’s ouster of Islamist President Mohammed Morsi rocked Egypt.

In the wake of the Herald story, a State Department spokeswoman admitted yesterday that Kerry was “briefly” aboard his $7 million luxury craft, the Isabel, on the day of the coup, after previously insisting the yacht sighting was “completely inaccurate.”

“While he was briefly on his boat on Wednesday,” State Department spokeswoman Jennifer Psaki said, “Secretary Kerry worked around the clock all day.”

The Herald front-page story captured a series of photos of Kerry paddling a kayak in shorts and a polo shirt. Then yesterday Obama posted his own kayaking photo on Twitter, tweeting, “Have a great weekend.”

It was unclear whether the president’s tweet was mocking Kerry or supporting him. The White House deferred comment to Organizing for Action, which runs Obama’s Twitter handle and did not return emails and calls for comment.

Meanwhile, Islamist protests over Morsi’s ouster erupted in violence that left at least 30 dead and more than 200 wounded.

Kerry’s vacation kerfuffle is being seen as the latest stumble in what has already been a rocky five months for the nation’s top diplomat.

“Kerry is having a pretty tumultuous tenure at the State Department,” Tom Whalen of Boston University said. “It seems everything he touches is not turning out well.”

Said Michael O’Hanlon of the Brookings Institution: “I’m not sure he’s really fully established himself as the go-to guy on foreign policy in the public’s eye here in the United States. I would think he’d want to define his leadership on some of the big crises of the day. Let him have his Fourth of July weekend, but recognize that this is an issue — Egypt — where he’s probably got to step up his game.”

Kerry’s team has insisted he’s been working full-time on Egypt.

On Wednesday alone, they said, he took part in a National Security Council meeting with the president and called dignitaries from Norway, Qatar, Turkey and Egypt, as well as placing five calls to Ambassador to Egypt Anne Patterson.