Israel, which quit the Gaza Strip in September after 38 years of occupation but controls the territory's borders, has been under US pressure to clear Palestinians for trade and travel, seen as a step to encourage peacemaking.
Some 1.4 million Palestinians live in the strip captured by Israel in the 1967 Middle East war.
Israel had accepted an Egyptian proposal to let Palestinians travel freely via the Rafah terminal, but with foreign oversight - a role to be filled by the EU monitors.
However, Israeli political sources said the European Union had balked at Israel's demand that its monitors arrest anyone suspected of smuggling arms from Egypt to Gaza militants.
Palestinians have objected to Israel's demand for cameras to film those who use the Rafah crossing, though they have welcomed an EU role to help reopen the terminal largely shut since Israel completed its Gaza pullout nearly two months ago.
"Israel wants the EU to have powers of arrests should its inspectors encounter a terrorist at the crossing. The EU wants to limit its role to oversight and reporting only," an Israeli political source said.
"This, added to the fact that there is still no clear agreement between Israel and the Palestinians on the matter, meant the cabinet vote was put off," the source said.
The EU's Middle East envoy, Marc Otte, said after meeting Palestinian officials in the West Bank that the EU was ready to play a "third party" role at the crossing and monitor both Israeli and Palestinian operations there.
But Otte said it was "too early to start negotiating the details" of an EU role at the crossing before Israel and the Palestinians agreed on the terms for reopening the terminal.
"Obviously what we will not be doing is taking the place of the Palestinian customs and security officials. In the end the Palestinian Authority will be in charge of its borders," he added.
An EU official in Tel Aviv said an EU delegation would address the issue with Israeli Vice Prime Minister Shimon Peres.