Senator Hillary Clinton has argued that the US administration's current stance on family planning may be increasing the number of abortions in the country.
Hillary Clinton says Mr Bush's policies may be increasing abortions
She said there could be a link between a decline in so-called "comprehensive" sexual education and an increased number of terminations.
It is unclear however if abortion rates have gone up or down under Mr Bush.
Since taking office in 2001, he has tightened legislation regulating terminations.
He has also boosted funding for sexual abstinence programmes which are not allowed to promote contraception.
On Monday, Mr Bush told anti-abortion campaigners marking the anniversary of a ruling which legalised abortion that the US was making progress towards reducing the number of terminations.
Speaking to a conference of pro-choice supporters in New York, Mrs Clinton said that during her husband's administration, family planning funding was a priority and "we saw the rate of abortion consistently fall."
"The abortion rate fell by one quarter between 1990 and 1995, the steepest decline since Roe was decided in 1973," Mrs Clinton said, referring to the Roe v Wade decision which legalised abortion.
"The rate fell another 11 percent between 1994 and 2000."
Mrs Clinton, who is considered a likely candidate for her party's presidential nomination in 2008, called for increased funding for family planning services and said she looked forward to a day when abortion was "truly safe, legal and rare."
And in comments seen as reaching out to those who oppose abortion, she also praised the influence of "religious and moral values" on delaying teenage girls from becoming sexually active.
In response to Mrs Clinton's comments, White House spokesman Ken Lasaius said the president believed in co-operation on the abortion front.
"He's made it very clear that whether we agree or disagree on the issue of abortion, that we can all work together to take practical steps to reduce the number of abortions that occur," Mr Lasaius said.