Washington, DC (LifeNews.com) -- A new poll sponsored by the Washington Post and ABC News has pro-abortion presidential candidates Hillary Clinton and Rudy Giuliani racing to stronger leads nationwide. Surveys in the top primary states give the advantage to Clinton on the Democratic side, but they show Mitt Romney leading in most of the early GOP contests.

The Post/ABC poll has former New York mayor Rudy Giuliani leading all candidates with the support of 34 percent of Republicans and far ahead of former Sen. Fred Thompson, who stands at 17 percent.

The survey has Arizona Sen. John McCain at 12 percent and former Massachusetts Gov. Mitt Romney at 11 percent.

Other Republican polls during the month of September have Giuliani leading by anywhere from two to eleven percent over his rivals but a new Rasmussen Reports survey also released Wednesday shows Thompson ahead by two points over the ex-mayor and Romney in third place instead of fourth.

Despite the new poll, surveys in leading primary states show Mitt Romney continues to outpace his opponents.

Romney leads by an average of 9 percent in the last four Iowa polls, although the most recent one has him ahead of Giuliani by just one point. The surveys show Giuliani in second and Thompson in third.

In New Hampshire, Romney leads the last six September surveys by almost four percent with Giuliani second and McCain third.

And in South Carolina, Romney has a three percent lead in the most recent poll, but Thompson led in three prior ones.

On the Democratic side, the new Post/ABC poll shows New York Sen. Hillary Clinton leading pro-abortion Illinois Sen. Barack Obama by a 53 to 20 percentage point margin. John Edwards, the former senator, runs a distant third with the support of 13 percent of Democrats.

State polls on the Democratic side show a closer contest.

In Iowa, all three top candidates are close, with Clinton holding a small lead but all three within the margin of error of some polls.

But in New Hampshire and South Carolina, Clinton has double digit leads over Obama and Edwards trails them both by another 5-10 percent.