WASHINGTON — Gender politics emerged as Hillary Rodham Clinton kicked off a book tour Tuesday that could preview a presidential run when she recalled her refusal to attack Sarah Palin’s selection as the Republican vice presidential candidate in 2008.

Clinton’s tour for “Hard Choices” began Tuesday morning in the friendliest possible setting: a book-signing event at a Barnes & Noble in Manhattan’s Union Square. Around 1,000 people – some had slept on the sidewalk – let out whoops as she arrived about 20 minutes behind schedule and delivered brief remarks with a patriotic tone reminiscent of the campaign trail.

The former secretary of state said the book was “written for anybody who wants to think about, and learn about, what is happening in the world today – why America matters, and why the world matters to America. And we have a lot of hard choices ahead of us in our country to make it as brave and as strong as it should be. And we have a lot of hard choices to continue to lead the world and solve problems that affect us and the rest of humanity.”

The book tour was scheduled to take Clinton to Chicago, Philadelphia, Washington, Toronto and Austin. Her frenetic pace and intense media attention resembled a hybrid of celebrity book tour and campaign kickoff, with plenty of hints of a presidential run.

In one of her first promotional interviews, Clinton was asked Tuesday on NBC about a 6-year-old tale she recounted in her book about 2008 Republican presidential nominee John McCain’s pick of Palin as his running mate. Clinton said Democratic candidate Obama’s campaign, which had defeated her bid for the nomination that year, asked her to attack Palin.

“I said, ‘Attack her for what? For being a woman?’ ” Clinton said. She said she told the Obama campaign there “will be plenty of time to do what I think you should do in politics, which is draw distinctions.”

Palin tweeted out the book’s account of the episode on Monday and accused the Obama campaign of firing “the 1st shot in the real ‘war on women.’ ” Republicans have pushed back on Democratic charges that the GOP wages a “war on women” by promoting policies that are detrimental for women.

Obama’s campaign advisers did not want to discuss Clinton’s account on the record, but they confirmed that they asked for her help in responding to Palin and did so without Obama’s involvement. At the time, Palin cast herself as the candidate for supporters of Clinton’s failed bid for the Democratic nomination. “Hillary left 18 million cracks in the highest, hardest glass ceiling in America,” Palin said during the campaign.

“But it turns out the women of America aren’t finished yet, and we can shatter that glass ceiling once and for all.”

Several advisers to Obama’s 2008 campaign, speaking anonymously, said the campaign wanted Clinton to argue that the Republican platform was antithetical to women’s issues.