Another security source said that the advice was in part directed at expatriate employees of UNRWA, the UN relief agency for Palestinian refugees.
But UNRWA said it had no plans to withdraw its foreign nationals.
"Christar Nordahl, deputy director in Gaza, confirmed receiving a general advice from Palestinian preventive security about a general kidnap threat," 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."
Foreigner abductions have been fairly common in the impoverished territory, with 20 foreign nationals abducted over the past year.
In most cases, the abductors used the hostages as bargaining chips for concessions from the Palestinian Authority and the detainees were released unharmed within days.
Palestinian colleagues of Razuri have meanwhile said his life was in danger because he needed medicine for heart disease.
Sakher Abu El-Awn, Gaza office manager of AFP, said Razuri was taking several types of medication, including for a heart problem.
"We believe his life is at serious risk and we urge his captors to release him immediately," Abu El-Awn told Reuters.
"He has been without his medicine for three days. He is supposed to be under a strict food programme because of his health condition."