(CNN) -- By a narrow margin of about 4,300 votes, Arizona voters approved a ballot measure that would legalize medical marijuana, state election officials said Sunday.

With all precincts reporting, the "yes" votes on Proposition 203 have 50.1 percent of the vote to 49.8 percent of "no" votes, according to unofficial results posted on the Arizona Secretary of State's website. More than 1.6 million votes were cast.

Officials in Maricopa County, where the city of Phoenix is located, posted their final update to the unofficial results from the November 2 election on Saturday. At the time, authorities said the race was too close to call.

The Marijuana Policy Project, in a statement, heralded the vote, saying it will allow patients who suffer from cancer, AIDS and other illnesses to use medical marijuana with a recommendation from their doctor.

"Voters in Arizona have sided with science and compassion while dealing yet another blow to our nation's cruel and irrational prohibition on marijuana," said Rob Kampia, Marijuana Policy Project executive director, in the statement. "Arizona's law now reflects the mainstream public opinion that seriously ill people should not be treated like criminals if marijuana can provide them relief, and that doctors should be able to recommend marijuana to patients if they believe it can help alleviate their suffering."

The Marijuana Policy Project provided funding and support to the Arizona Medical Marijuana Policy Project, the group that ran the Proposition 203 campaign, the group said. The national organization bills itself as the United States' largest marijuana policy reform organization, and says on its website it would like to see marijuana regulation similar to that of alcohol.

Since 1996, 14 other states and the District of Columbia have passed medical marijuana laws.

The proposition will allow the establishment of about 120 state-regulated clinics to dispense marijuana, according to the organization. Those living more than 25 miles from a clinic will be allowed to grow their own medicine.

CNN's Nick Valencia contributed to this report.