That proposal, opposed by ruling militant group Hamas, would implicitly recognize Israel.
Abbas set the date of the vote as July 26.
He made the declaration despite pleas by the ruling Hamas party to hold off on a vote.
A senior Hamas lawmaker immediately rejected the decree. Mushir al-Masri called the decree "a declaration of a coup" against the Hamas-led government.
Opinion polls show Abbas is expected to win majority support for the creation of an independent Palestinian state.
Earlier, Hamas said it had formally ended a 16-month truce by firing rockets at Israel after shells thought to have been fired by Israeli forces killed seven people on a Gaza beach.
The dead included a young family.
The killings prompted Hamas to stage a series of large demonstrations late on June 9 across the Gaza Strip.
A Hamas spokesman, Sami Abu- Zuhri, said it could not "remain silent" after the deaths.
"Amid the continued bloodshed of our people and the horrific images of the children, the women, the girl that screamed for help, there is no place for silence," he said.
"These demonstrations are stressing the need for the renewal of the struggle" against Israel.
Hamas also declared three days of national mourning.
Israel has launched an investigation into the incident.Israeli Defense Minister Amir Peretz has sent a message to Abbas voicing "deep regret at the deaths of innocent people."
Israeli Foreign Ministry spokesman Mark Regev said on June 9 that "this Hamas statement about reinstating violence really came late because there is very clear evidence that over the last few days Hamas has been involved in a very direct way in the launching of rockets that have targeted our cities, targeted our civilians, our communities and this just has to stop."