NARAL argues that the advertisements contravene Google's policies on the grounds they are deceptive because they contain text that suggests they provide abortions when in fact they do not.
CPCs exist to provide information about abortion and alternatives, as well as counselling and support for women facing unexpected pregnancies.
NARAL reported that 79 per cent of the time someone searches Google for 'abortion clinic', adverts for CPCs appear.
Illyse Hogue, president of NARAL, said in the Washington Post that they did not object to the centres themselves, just their advertising.
"We have no problem with crisis pregnancy centres advertising online; we have no problem with their existing. That is their right in America," said Hogue.
However many working closely with CPCs argue that the advertisements are not deceptive because they do not claim to offer abortions, but rather information about abortions.
One advertisement highlighted by NARAL contained the headline "Abortion Informationâ€"is it safe? How much does it cost?" Another offered "Abortion Resources" and "Free & Private Info/Ultrasounds. Determine Viability/Gestational Age."
Debi Harvey, director of Open Arms Pregnancy Clinic in Northridge, California, said in World Magazine that in her experience it was "very rare" that CPCs would use deceptive advertising tactics.
While she did not contest that there may have been a handful of cases of this kind of abuse, she rejected any suggestion that it was widespread in the CPC community: "It grieves me that 'pro-choice' people are so blatantly disparaging pregnancy centres.
"They might find one exception, or two, or three, and then they publish a full-on report on how this is what all pregnancy centres do. They paint us with a very broad brush."
The pro-life media group Heroic Media, who in the current fiscal year have provided information on pregnancy support services to 200,000 people, called on Google to re-consider its decision, arguing that advertisements like theirs have the same goals as the work of Google generally.
Joe Young, Vice President of Operations and Strategic Initiatives said: "Every day Google empowers individuals worldwide with information to make all sorts of decisions.
"In the same way, Heroic Media's advertising empowers women by helping provide honest, medically accurate information about abortion as well as support services available to them.
"We encourage Google to remain neutral in their stance on this issue by applying the same standards to crisis pregnancy centres' advertising as every other industry or organization, including abortion providers."
While NARAL and other pro-life organisations have pointed to several private investigations of CPC advertising, government investigations have not found the reported deceptions NARAL claims to exist.
When pro-choice California representative Henry A Waxman requested an official investigation into the advertising practices of CPCs in 2006, the official report published in response concluded that out of 2,500 counselling centres examined, only 25 were guilty of fraudulent advertising.
Brian Fisher, co-founder and president of Online for Life, defended the activities of the vast majority of CPCs in World Magazine: "Our observation is that an overwhelming number of pro-life groups only advertise that women have options, and that they should consider those options."
In a circular e-mail sent by NARAL, the group celebrated their victory: "Google's leadership in removing the majority of these ads is a victory for truth in advertising. Countless women will be spared lies and shaming tactics intended to stop them from making their own decisions based on real medical advice."
National Right to Life Committee President, Carol Tobias, said to US Political news website TheHill.com that: "Google is waging a war on women by limiting knowledge of the options and services available to women.
"Google's decision to refuse ads by the centres is unconscionable."
In 2008, Google reached an out of court settlement with pro-life religious groups in the UK who were having advertising relating to their content censored. After reviewing their policies, Google relented and permitted the advertisements to go ahead.
At that time, Google said: "We have decided to amend our policy, creating a level playing field and enabling religious associations to place ads on abortion in a factual way."
The conservative political activism website ActRight.com, has launched an petition on the CitizenGo service calling for Google to reverse its decision.
The petition calls on potential signatories to "let Google know that you oppose their banning of ads because of pro-abortion political pressure".
It has so far gathered over 10,800 signatures.