WASHINGTON (CNN) -- Sen. Hillary Clinton, D-New York, and former New York City Republican Mayor Rudy Giuliani hold leads in the contest for each party's 2008 presidential nomination, a new CNN/Opinion Research poll finds.

When registered Democrats were asked whom they would favor for their party's presidential nomination next year, more than a third (34 percent) cited Sen. Hillary Rodham Clinton of New York.

She was followed by Sen. Barack Obama of Illinois (18 percent); Sen. John Edwards of North Carolina (15 percent); former Vice President Al Gore (10 percent); Sen. John Kerry of Massachusetts (5 percent); and Sen. Joseph Biden of Delaware (3 percent).

Trailing with 1 percent or 2 percent were retired Gen. Wesley Clark, Rep. Dennis Kucinich of Ohio, New Mexico Gov. Bill Richardson; Sen. Christopher Dodd of Connecticut; the Rev. Al Sharpton and Iowa Gov. Tom Vilsack.

The poll has a sampling error of 4.5 points.

Among Republicans, former New York Mayor Rudy Giuliani was in the lead, with 32 percent citing him; followed closely by Sen. John McCain of Arizona, who garnered 26 percent.

Following them were former Speaker of the House Newt Gingrich of Georgia (9 percent); Massachusetts Gov. Mitt Romney (7 percent); former Virginia Gov. James Gilmore (3 percent); former New York Gov. George Pataki (3 percent); Sen. Sam Brownback of Kansas (2 percent); and Sen. Chuck Hagel of Nebraska (2 percent). One percent each was recorded by former Arkansas Gov. Mike Huckabee, Rep. Duncan Hunter of California, Rep. Ron Paul of Texas, Rep. Tom Tancredo of Colorado, and former Wisconsin Gov. Tommy Thompson.

This part of the poll had a sampling error of plus-or-minus 5 points.

The poll comes on the 34th anniversary of the U.S. Supreme Court's Roe versus Wade decision, which made abortion legal in all 50 states.

Asked whether the decision should be overturned, 29 percent said yes; 62 percent said no. The sampling error was plus-or-minus 3 points.

Full poll results