The United States has warned its citizens to avoid travel to Israel, and to leave the Gaza Strip immediately.
October's attack was the first time a US target has been hit in Gaza
A State Department statement said that the Islamic militant group Hamas had made threats against US interests.
Two Hamas leaders have been killed in recent weeks by Israel, and the US says the situation "remains extremely volatile".
The warning came shortly before a blast partially destroyed the home of the Gaza police chief in Gaza City.
No one was hurt in the pre-dawn explosion, Palestinian police and witnesses said.
There has been no immediate comment on the explosion by the Israeli military.
"The Department of State warns US citizens to depart Gaza immediately and to defer travel to Israel, the West Bank and Gaza due to current safety and security concerns," the statement said.
Hamas has vowed a "volcano of revenge" against Israel
"Statements have been made by Hamas elements and other terrorist Groups threatening revenge against US interests following the killings of Hamas leaders in Gaza, which could include kidnappings," it continued.
The statement said American citizens "should avoid, to the extent possible, public places such as restaurants and cafes, shopping and market areas and malls, pedestrian zones, public buses and bus stops, and other crowded venues".
Wednesday's statement updated a travel warning from 23 March, which was issued on the day Israel assassinated Hamas spiritual leader Sheikh Ahmed Yassin.
It now refers to Hamas threats to avenge the 17 April killing of his successor Abdel Aziz al-Rantissi.
Last October, three US security personnel were killed when a diplomatic convoy was targeted in Gaza.