The gunmen have not been identified; but Al Jazeera reported that Abbas's Preventative Security Forces had officially blamed the Hamas-allied Executive Security Force for the attacks.
Before the ambush, the security officers had stormed a house where they believed a colleague, who had been kidnapped earlier in the day, was being held, security officials said in a statement.
The officers were attacked and one was injured.
They were then attacked again as they drove the injured man to hospital, the statement said.
According to witnesses, the official's car was attacked with bullets and a rocket-propelled grenade.
Earlier on Wednesday, a woman caught in crossfire between Fatah and Hamas gunmen at a refugee camp in northern Gaza was shot in the head and seriously wounded.
Several violent incidents in recent days have raised concerns that the ceasefire agreement may be threatened.
Odeh said: "These incidents only serve to reiterate how fragile the ceasefire is."
The incidents come as security forces continue to search for an AFP photographer abducted on Monday.
"These incidents only serve to reiterate how fragile the ceasefire is"
Al Jazeera correspondent
Palestinian security officials earlier advised foreign nationals to leave Gaza due to kidnap threats.
Security officials said they had advised American and European nationals to leave because of a threat of further abductions.
Another security source said that the advice was in part directed at expatriate employees of UNRWA, the UN relief agency for Palestinian refugees.
UNRWA confirmed that it had received advice from the Preventative Security Force about the kidnap threat but said it had no plans to withdraw its foreign nationals.
Johan Eriksson, UNRWA spokesman, said: "In our view, this doesn't change the situation from what it has been in the past two years ... at the moment we are staying put."