THERE was a quiet gesture of intimacy when Hillary Clinton and Michelle Obama teamed up for an awards ceremony for women at the State Department last week. In an unscripted moment away from the cameras, Clinton reached out and gave the first lady's hand a squeeze.

Like Clinton before her, Michelle Obama has had to go out to bat for her husband after his popularity hit a rough patch. "I believe in this nation and I believe in my husband," she said in her first television interview as first lady as a poll showed Barack Obama's approval ratings had slipped below George W Bush's at the same stage of his presidency.

The two first ladies have become best "frenemies" after their stand-off on the campaign trail, where Michelle Obama accused Clinton of presuming she was the "inevitable" candidate.

"I know a little bit about the role that Michelle Obama is filling now," Clinton said to laughter at the meeting, before going on to praise "her grace and her wisdom".

Not only do the presidential spouses have much in common, but Clinton herself has been behaving uncannily like a first lady again in her new role as secretary of state. As she tours the world and welcomes foreign dignitaries to Washington, Clinton has been acting as booster-in-chief to Obama, much as she did for her husband Bill Clinton during the ups-and-downs of his presidency.

She has repeatedly quoted Obama's phrases approvingly, such as "reaching out a hand" to Iran if the mullahs "unclench their fist", and emphasised that it is a "privilege" to serve in his administration.

Almost every official visit is a trip down memory lane, meeting a "dear old friend" such as Tony Blair or the Israeli president Shimon Peres, whom she encountered many times as first lady.

"She is reflexively playing second fiddle but also trying to justify her importance," said Sally Bedell Smith, author of For Love of Politics, an account of the Clintons' White House years.

The Washington Post admonished Clinton last week for refusing to take human rights seriously. Asked in Egypt whether a recent critical State Department report of the country would affect relations with the Egyptian president, she said she hoped to see him often in Cairo and Washington.

"I really consider President and Mrs Mubarak to be friends of the family," Clinton replied.

In Japan, she greeted Hirofumi Nakasone, the foreign minister, with an affectionate reference to a photograph showing them meeting 18 years ago.

In China, she recalled staying at the "very same guest house that my husband and I stayed in" in the 1990s.

Meanwhile, Clinton has delegated the world's trouble spots to special envoys - mostly old hands from her husband's administration such as George Mitchell in the Middle East, Richard Holbrooke in Afghanistan and Pakistan, and Dennis Ross, who has been given responsibility for the euphemistically named "Gulf and Southwest Asia", otherwise known as Iran.

A foreign policy analyst at a leading think tank in Washington said: "She's happy to get the hard work done by the special envoys while she gets to do the foreign trips and be Mrs America."

Another foreign policy expert claimed: "There have never been so many special envoys. At this rate, she will be left with the handshakes and funerals. It is storing up a lot of bureaucratic trouble."

Bedell Smith thinks, on the contrary, that Clinton is shrewd to reprise her old role: "She can blame the special envoys for what goes wrong and take the credit for what goes right, while she does the meetings and greetings."

Obama appointed Melanne Verveer, a former chief of staff to Hillary Clinton in the White House, as ambassador for Global Women's Issues last week, reflecting the importance at the State Department of a cause Clinton championed as first lady.

The former first lady has not forsworn all presidential ambition. Ann Lewis, a confidante and long-time adviser, has set up an organisation called No Limits - "inspired by Hillary" - which will keep her supporters and infrastructure in play, should there be an opportunity to run for the White House again.

"Hardcore Hillary supporters are fully expecting her to run again in 2016," an official with "deep Clinton ties" told The New York Times.

The economic crisis is taking a toll on Obama's popularity. Only 56% of Americans approve of his performance, according to a poll by Rasmussen last week, compared with 43% who disapprove. A third "strongly" disapprove.

"This is a substantial degree of polarisation so early in the administration. Mr Obama has lost virtually all of his Republican support and a good part of his independent support," Scott Rasmussen and Douglas Schoen, a former pollster for Bill Clinton, noted in The Wall Street Journal.

Michelle Obama has emerged as one of the strongest advocates for her husband. On a visit to Fort Bragg, an army base in North Carolina, she said, "It hurts, it hurts", to see military families on food stamps.

"I think right now people understand that we're going to have to all work together and make a set of sacrifices. And they have faith - as I do - that their commander-in-chief will see us through these times."