A new CBS News poll released Sunday found that "71 percent of Alabama Republicans say the allegations against Roy Moore are false," according to a CBS News release.
Meanwhile, another poll that was conducted by The Washington Post and George Mason University and released Saturday found the two candidates neck and neck.
The poll by the Post and George Mason University found that 50 percent of likely voters support Jones, a former prosecutor, versus 47 percent for Moore, a former judge, a slight three-point difference barely a week ahead of the election.
In the same poll, 53 percent of the voters said they consider Jones to have higher standards of moral conduct than Moore, the Post reported.
"In contrast, about a third of likely voters say Moore, who has cast his campaign as a 'spiritual battle' with heavy religious overtones, has higher moral standards," the Post said.
The CBS News survey released today found that most Republican voters, 53 percent, say that while they are concerned about the allegations against Moore, other issues are of greater importance.
Half of Moore's supporters say they back him because they want a conservative in the Senate "rather than because they think Moore is the best person for the job," the CBS News release said.
A senior adviser to the Moore campaign commented on the CBS News poll Sunday.
"The only poll that matters is Election Day, but the trend indicates momentum," Moore adviser Brett Doster said. "Those who know Roy Moore best know the allegations are false and part of a political attack. We will win next Tuesday."
ABC News' Tom Llamas contributed to this report.