Updated

After the Sept. 11 attacks on the World Trade Center (search), then New York City Mayor Rudy Giuliani (search) was commonly referred to as "America’s Mayor." The latest FOX News poll finds that many Americans remember Giuliani's leadership in a time of crisis and rate him higher than several other potential 2008 presidential contenders as a "strong and decisive leader." In addition to candidate attributes, the new poll also looks at some possible presidential matchups for the next election.

Almost two-thirds of voters (65 percent) think Giuliani is a "strong and decisive leader," and majorities think that characterization also applies to Sen. John McCain, R-Ariz., (56 percent), Sec. of State Condoleezza Rice (55 percent), President Bush (51 percent) and Sen. Hillary Clinton, D-N.Y. (51 percent). Sen. John Kerry, D-Mass., and former Vice President Al Gore (search) come in well below the others, with majorities saying the term "strong and decisive leader" does not apply to them.

In pre-election polling, Bush consistently bested Democratic challenger Kerry on the strong leader quality. In this week’s poll, 51 percent say they think Bush is a strong leader and 46 percent say he is not, while 35 percent think the term describes Kerry and 56 percent disagree.

Among Democrats, 76 percent think the term "strong leader" applies to Clinton, 60 percent to Kerry and 45 percent to Gore. Just over half of Democrats think the trait is true for McCain (52 percent) and Giuliani (51 percent), while fewer than one in five think so for Bush (16 percent).

Republicans overwhelmingly think "strong leader" is true of Bush (91 percent), and large majorities also think so for Giuliani (78 percent) and Rice (76 percent). Hardly any Republicans think Kerry (10 percent) and Gore (9 percent) are strong leaders, though more than one in five think Clinton is (22 percent).

Clinton, McCain and Giuliani also do well on the trait of "understands the needs of average Americans." Here again, more than six in 10 voters (63 percent) think that characteristic applies to Giuliani, and over half think McCain (57 percent) and Clinton (53 percent) understand average Americans.

Round up of 2008 Presidential Matchups

It has been less than a year since the last presidential election, so needless to say the matchups in this poll are hypothetical. Here are some highlights:

Among Democrats, Clinton has a sizeable advantage over other possible contenders as that party’s nominee for the 2008 presidential race. For Republicans, Giuliani and McCain top the party’s primary preference list — both receive about equal levels of support.

Giuliani tops by double digits each of the three Democrats he was tested against (Clinton, Kerry and Gore). Among the Democrats, Clinton does best against Giuliani.

On an all female ticket, Clinton tops Rice by 3 percentage points (within the poll’s margin of error). Women divide their vote 49 percent Clinton and 41 percent Rice, while men are slightly more likely to back Rice (46 percent) over Clinton (43 percent).

"I think the most interesting thing about these results is that while Giuliani and McCain both stack up well against Democrats at this point, they both have problems with the rightwing and fundamentalist segments of their party," comments Opinion Dynamics Chairman John Gorman. "The question for them is: can they be nominated?

"On the other hand, Clinton scores fairly well and the nomination issue doesn’t seem as difficult. If she is nominated to oppose a lesser known Republican candidate after Giuliani and McCain have been rejected by their party, she might look much stronger."

Opinion Dynamics Corporation conducted the national telephone poll of 900 registered voters for FOX News on September 27-28.

• PDF: Click here for full poll results.