Dubai police say at least 11 suspects in the killing of al-Mabhouh used altered British, Irish, French and German passports.
Britain, Ireland and France have already summoned Israeli diplomats to seek information on possible Israeli involvement.
Relations at risk
Although the EU is not directly responsible for passport issues, which are under the individual jurisdiction of its 27 members, it is likely to support any measures that the affected nations may propose.
A senior EU diplomat said Israel's suspected role in the murder of al-Mabhouh and the killers' alleged use of forged EU passports would threaten relations with the European bloc.
"The passport controversy obviously will be harmful for the way Israel is treated by the EU," the official, who asked not to be named because of the sensitivity of the issue, said.
Separately, the British embassy in Israel said on Sunday it was giving new passports to six British nationals whose identities were stolen by the suspects.
Izzat al-Rishq, a Hamas official, told the Jordanian newspaper Al-Sabeel that the group "has formed a high-level investigation committee" to try to discover "how the Mossad was able to carry out the operation".
In Dubai, Anwar Gargash, the UAE's minister of state for foreign affairs, voiced concern on Sunday that the assassins used expertly doctored passports from nations that do not require advance UAE visas, allowing them to enter the country without scrutiny.
Sheikh Abdullah bin Zayed Al-Nahyan, the foreign minister, urged European allies to investiigate how fraudulent passports had been used by the hit squad.
Emirati officials close to the investigation said that at least two more suspects in the murder entered the country on fraudulent Irish passports.
They also said some of the 18 suspects visited the Gulf city state for a reconnaissance mission at least once before the slaying.
The UK Sunday Times newspaper reported on Sunday that Binyamin Netanyahu, Israel's prime minister, allegedly given the green light for the assassination.
The paper, citing "sources with knowledge of Mossad", said Netanyahu visited the Israeli intelligence headquarters in early January and, after being briefed, authorised the killing of al-Mabhouh.
A rehearsal of the operation, which reportedly involved at least 18 agents, was apparently carried out at a Tel Aviv hotel - without detection - prior to the briefing, The Times reported.
Hamas has acknowledged that al-Mabhouh smuggled weapons for it. The Palestinian group rules the Gaza Strip after seizing control from its rival Fatah in 2007. It is also opposed to Israel's existence as an independent state.