"During the meeting (on Saturday evening), updates were exchanged between the parties, and transfer of information was agreed upon by way of additional meetings to take place in order to further track the issue," said COGAT, the defence ministry unit responsible for Palestinian civilian coordination.
One proposal to combat the disease was for Israel to provide courses in advanced epidemiology for Palestinian and Jordanian medical staff, a health ministry official said on condition of anonymity.
Ebola has killed more than 4,000 people this year, nearly all of them in the West African countries of Liberia, Guinea and Sierra Leone, according to the World Health Organisation (WHO).
"There are contacts with the Israeli side regarding this within the context of WHO's instructions on fighting this virus, which is a global task," said Assad Ramlawi of the Palestinian health ministry.
"There are common crossings and we have contacts on this, nothing more or less," he told AFP.
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Israeli Prime Minister Benjamin Netanyahu held a meeting Sunday with health, military, police, border crossings and other relevant officials over the epidemic.
"We are taking a certain number of measures to isolate any sick people from countries at risk and to treat them of course," Netanyahu said in a statement. "This is a global epidemic and we are cooperating with other states."
Efforts to counter the spread of the disease would focus on border crossings and Ben Gurion International Airport, near Tel Aviv, said the statement.
There have been no reported cases of Ebola in Israel or the Palestinian territories.
Israel is a popular destination for African Christians, with around 43,000 of them having visited the country since the start of the year, according to the tourism ministry.