"Those who think that street-based hate crimes should have precedent over online ones, should realize there is no competition in getting access to justice", he said, according to the Independent.
Saunders said she hopes the new plans will see more prosecutions, with longer sentences for those convicted if a jury or judge can be convinced the crime was motivated by hate.
Saunders says that the new guidelines, along with existing provisions, will offer a better deal to the victims of online abuse and ensuring they have more support and protection - whoever they might be.
Saunders said the crackdown is needed because online abuse can lead to the sort of extremist hate seen in Charlottesville in the U.S. last weekend, which left one person dead.
The CPS now says prosecutors should pursue online cases of abuse with the same "robust and proactive approach used with offline offending".
Alison Saunders, the Director of Public Prosecutions, said: "Hate crime has a corrosive effect on our society and that is why it is a priority area for the CPS".
"Left unchallenged, even low-level offending can subsequently fuel the kind of unsafe hostility that has been plastered across our media in recent days".
"We should remember that there is a less visible frontline which is easily accessible to those in the United Kingdom who hold extreme views on race, religion, sexuality, gender and even disability", she wrote in The Guardian.
"In order to spread the new policy and encourage victims of hate crimes online and off to come forward and report the incidents, CPS also launched a social media campaign called "#HateCrimeMatters".
Rising levels of hate crime in Britain have been highlighted since the European Union referendum last year, with reports soaring in the month after the vote by 41% - equivalent to 5,468 more crimes recorded than on the same month in the previous year.
"We commit to treating online hate crimes just as seriously as those experienced face to face", she said.
The CPS announcement is particularly topical in light of the recent violence in Charlottesville in the U.S., and is part of a bigger-picture government push to address hate crime that began last summer.
The new policy covers different strands of hate crime: racist and religious; disability; and homophobic, biphobic and transphobic. Online hate crime is every bit as serious as any other kind, and all too often spills over into the "real" world.