Authorities have been using immigration records and CCTV-captured images of the suspects to try to piece together what happened in the hours before al-Mabhouh's murder.
Al-Mabhouh was found dead in a luxury hotel in Dubai on January 20.
Police in Dubai have accused Mossad, Israel's intelligence and espionage agency, of carrying out the killing.
The Israeli government has neither confirmed nor denied any role in the incident, saying it has a "policy of ambiguity" on covert operations.
Hamas has acknowledged that al-Mabhouh smuggled weapons for it.
The Palestinian group, which is opposed to Israel's existence as an independent state, rules the Gaza Strip after seizing control from its rival Fatah in 2007.
A senior Hamas official, meanwhile, dismissed suggestions that someone within the group had leaked information about al-Mabhouh's whereabouts endangering his life.
"Some people are trying to say that there was leak inside Hamas [but] we don't accept that," Osama Hamdan told Al Jazeera on Tuesaday.
"We've information that we can share with the authorities and that information clarifies how the Israelis got inside but not through a leak inside Hamas."
The previously named British suspects have all been found to be UK citizens living in Israel, and each claims their identities was stolen.
The use of stolen or faked passports to carry out extrajudicial killings has drawn heavy criticism from Israel's European allies, with all four nations involved summoning their respective Israeli ambassadors for answers.
The European Union on Monday issued a short statement saying that al-Mabhouh's assassination was "profoundly disturbing" and that its citizens' rights had been violated.
"The EU strongly condemns the fact that those involved in this action used fraudulent EU member states' passports and credit cards acquired through the theft of EU citizens' identities," it said.
However, no direct mention of Israel was made in the statement.