(CNN) - A new poll of those who watched Tuesday's presidential debate shows results largely in line with the CNN/ORC International survey of debate watchers conducted the night of the matchup.
Gallup found debate watchers thought President Barack Obama performed significantly stronger this week than he did in his first debate. In a 13-point split, 51% said Obama won and 38% gave the win to Republican challenger Mitt Romney. One in 10 said neither candidate won.
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Independents broke 54% for Obama and 33% for Romney, Gallup found.
The separate CNN survey conducted on Tuesday night showed those who watched the Hempstead, New York face-off leaned towards Obama, 46% to 39%, although the seven-point difference was within the sampling error of plus or minus 4.5 points.
Both campaigns claimed victory Tuesday night and in the days which followed. The debate was moderated by CNN Chief Political Correspondent Candy Crowley.
The breakdown was significantly different from the Gallup poll following the first presidential debate, on October 3. Seventy two percent said Romney won, while only 20% gave Obama the win.
The CNN poll conducted after the first debate also showed a Romney win.
Friday's Gallup poll included telephone interviews conducted between October 17 and 18 of 813 adults who say they watched Tuesday's debate. It has a sampling error of plus or minus four points.
The next debate will be held Monday in Boca Raton, Florida and will focus on foreign policy and national security.
- CNN Political Editor Paul Steinhauser contributed to this report