US Secretary of State Hillary Clinton leaves New York Presbyterian Hospital with husband, Bill, and daughter, Chelsea, in New York, on Wednesday. [Photo/Agencies]

Secretary of state keen to resume work, top aid says.

US Secretary of State Hillary Clinton left a New York hospital late on Wednesday after three days of treatment and is expected to make a full recovery from a rare blood clot in her head.

"Secretary Clinton was discharged from the hospital this evening," a top aide, Deputy Assistant Secretary Philippe Reines, said in a statement, after the 65-year-old diplomat was forced to spend New Year's Eve in a hospital bed.

"Her medical team advised her that she is making good progress on all fronts, and they are confident she will make a full recovery," he said, adding that Clinton was "eager to get back to the office".

Earlier the top US diplomat, bundled up against the cold in a thick winter coat and wearing dark glasses, appeared in public for the first time in almost a month when she came out of a building at the New York Presbyterian Hospital.

It was the first time Clinton had been seen since catching a stomach virus on returning from a trip to Europe on Dec 7, which triggered a series of health scares, forcing doctors to order her to rest.

Accompanied by her smiling husband, former president Bill Clinton, as well as her daughter Chelsea and several aides, Clinton walked to a waiting black van at the hospital, according to images broadcast by CNN.

Both Clinton and her family "would like to express their appreciation for the excellent care she received from the doctors, nurses and staff at New York Presbyterian Hospital Columbia University Medical Center", Reines added.

He did not say when the secretary would return to work though, promising only to issue an update in the coming days. He did not specify where Clinton was going, but she has a home in Chappaqua, New York.

"Grateful my Mom discharged from the hospital and is heading home. Even more grateful her medical team confident she'll make a full recovery," Chelsea Clinton said in a tweet.

The health scare, which has grounded the normally indefatigable secretary of state, came as she prepares to step down after four years in office later this month.

She will most likely hand the baton to Senator John Kerry, who has been nominated by President Barack Obama to replace her.

Kerry's appointment will have to be confirmed by the new Senate, due to be sworn in on Thursday, but as a veteran, well-respected senator, he is expected to sail through his confirmation hearing.

Clinton has been largely credited with helping to restore US' image abroad in the past four years, and Obama has said that he had begged her to stay on.

But the former first lady and senator has admitted to being exhausted after being in the public eye for almost two decades. As secretary of state she has flown almost 1.6 million kilometers and visited 112 countries, tirelessly promoting democracy and what she calls "smart power".

Earlier, State Department spokeswoman Victoria Nuland said that despite her illness Clinton had been busy keeping in touch by telephone.

"She has been talking to her staff, including today. She's been quite active on the phone with all of us," Nuland told journalists.

The globe-trotting diplomat was admitted to the hospital on Sunday after a routine scan revealed the clot in a vein behind her right ear in the space between her skull and her brain.

Her doctors Lisa Bardack, from the Mount Kisco Medical Group, and Gigi El-Bayoumi, of George Washington University, said in a statement on Monday that Clinton had not suffered a stroke or any neurological damage.

They said however they would be treating Clinton with blood thinners to break up the clot, which if left untreated could be potentially dangerous.

The blood clot is believed to have stemmed from a concussion, which happened when Clinton became dehydrated as a result of the stomach bug and fainted.

The illness has raised questions about Clinton's political future and how her health might influence her decision about whether to run for president in 2016, as prominent Democrats have been urging her to consider.

Clinton still has some unfinished business as she wraps up her tenure at the State Department, and is widely expected to testify before the end of the month on the Sept 11 attack on a diplomatic mission in Libya.