DES MOINES, Iowa — Senator Clinton, unbowed by a third-place finish in the Iowa Democratic caucuses, hailed a “great night for Democrats” and said the strong turnout pointed for sure to the election of a Democratic president in November. She said she would “keep pushing as hard as we can.”

The former first lady, who had once held a commanding lead in polls here, congratulated caucus winner Senator Obama and the second-place finisher, a former senator, John Edwards. She promised cheering supporters she would take “this enthusiasm and go tonight to New Hampshire.” The state holds its primary on January 8.

“We’re going to keep pushing as hard as we can,” she said. Supporters chanted, “Hillary, Hillary.”

With President Clinton and their daughter, Chelsea, standing to one side of her and a former secretary of state, Madeleine Albright, to the other, Mrs. Clinton said, “I am so ready for the rest of this campaign and I am so ready to lead.”

“This is a great night for Democrats. We have seen an unprecedented turnout here in Iowa and that is good news because today we are sending a clear message that we are going to have change and that change will be a Democratic president in the White House in 2009.”

Projections showed a turnout of 220,588 for Democrats, compared to 124,000 who showed up for Democratic caucuses in 2004. The turnout was nearly twice as large as the Republican turnout, which was also up from four years ago.