Announcement caps day of street gun battles between Fatah and Hamas supporters and the killing of a security officer.
Odeh earlier said that the ceasefire instruction from the two factions would take time to reach fighters on the ground.
She said: “The ceasefire is on very shaky ground with the president and the cabinet [Hamas] exchanging blame.
Abbas told the news conference: “On Saturday, I called for early presidential and legislative elections. With the current impasse I felt it was essential to allow the people to have their say on a platform that achieves Palestinian national interests.
“We want to examine the will of the people. Do they still trust those they have chosen?”
Abbas said he was still open to the formation of a unity government of technocrats.
The West has sought to bolster Abbas, who favours a two-state solution to end conflict with Israel.
“We have been in a crisis for nine months. People cannot wait for long … People are suffering from the economic social and security situation”
Mahmoud Abbas, Palestinian president and leader of Fatah
Western sanctions have deeply affected the Hamas-led government.
An Israeli trade embargo has also severely limited the flow of funds through the occupied Palestinian territories.
“We have been in a crisis for nine months. People cannot wait for long,” Abbas said. “People are suffering from the economic social and security situation.”
Abbas called for increased international efforts to reach a permanent solution to the Palestinian-Israeli conflict, and said a meeting with Ehud Olmert, Israel’s prime minister, was necessary.
“We have to meet. We need each other, and we have to deal with our problems,” he said.
Reiterating his support for Abbas, Blair said the international community’s job was to “support the people of moderation”.
“If the international community really means what it says about supporting people who share the vision of a two-state solution, who are moderate, who are prepared to shoulder their responsibilities, then now is the time for the international community to respond,” Blair said.