Fatah blamed Hamas for the abduction.
Odeh said there had also been "abductions and counter-abductions by Fatah and Hamas".
A Palestinian security source said Hamas men abducted a total of nine Fatah activists on Monday.
Hamas said the abductions were triggered when Fatah seized one of its members.
Fatah sources said Hamas had said Abu Zaida would only be released in exchange for Emad Deeb, a Hamas official snatched earlier in northern Gaza. But Abu Zaydeh was released unharmed less than an hour later.
Five Fatah members and four Hamas loyalists were kidnapped earlier during the day in the north of the coastal strip, officials and witnesses told the Agence France Presse news agency.
Fighting escalated after Mahmoud Abbas, the Palestinian president and Fatah leader, called on Saturday for early elections, a move he said was intended to end a deadlock with Hamas and get Western sanctions lifted.
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.
"Religious leaders will visit both the president and the interior minister tomorrow in Gaza to see if a common ground can be reached."
Abbas said on Monday that plans for early elections will continue despite opposition from the Hamas-led government.
Speaking at a joint news conference, Tony Blair, the British prime minister, said it was critical that the international community supported Abbas in the coming weeks.
The leaders met in the West Bank city of Ramallah hours after the truce took effect in Gaza following heavy fighting between Fatah and Hamas forces.
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.
Western sanctions have deeply affected the Hamas-led government.
"We have been in a crisis for nine months. People cannot wait for long ... People are suffering from the economic social and security situation"
Palestinian President and leader of Fatah
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.