"Two British police officers arrived a few days ago to interview British passport holders on the use of false passports" bearing their identities in the case, Shamir told the AFP news agency.
The officers were preparing to meet six dual nationals whose British passports were used in the assassination, Britain's Serious Organised Crime Agency (Soca) said.
"We are arranging to speak to the six genuine passport holders who are resident in Israel as potential witnesses to a crime," Britain's Press Association news agency quoted a Soca spokesman as saying.
Identity of killers
The Dubai police have published details of 26 suspects together with passport photographs, and claims to have DNA evidence of the identity of at least one of the killers.
"What is sure right now is that the majority of the murderers whose names have been announced ... are to be found in Israel," Tamim, the police force's head, said in comments published in the Arabic-language daily Al-Khaleej.
"Dagan and Israeli Prime Minister Benjamin Netanyahu will head the list [of an international arrest warrant] if it is proven that Mossad is behind the murder," he said, referring to Israel's spy agency.
Israel has said there is no evidence of its involvement and has rejected the calls for Dagan's arrest as "baseless" and "absurd".
The murder of al-Mabhouh, regarded by Israel as a vital link in a weapons-smuggling chain into the Hamas-controlled Gaza Strip, has mounted international pressure on Israel.
Twelve British, six Irish, four French, one German and three Australian passports were used by the suspects, according to Dubai police.
Israeli ambassadors in four European countries have been summoned for talks and the European Union has also voiced outrage over the use of fake passports.
The revelation of stolen identities being used by suspected Israeli agents has caused a diplomatic outcry, with Australia threatening it would "not be silent on the matter".
Canberra summoned Yuval Rotem, the Israeli ambassador, on Thursday and said that friendly ties were at risk if Israel was found to have sponsored or condoned the tampering of the Australian passports.
The spotlight is also falling on those countries where police say the alleged assassins' trails begin and end: Switzerland, Italy, France, Germany and the Netherlands.
Authorities there have either declined to say whether they are investigating, or told the Associated Press news agency that they have no reason to hunt down the 26 suspects.
European countries' reluctance to investigate may have something to do with the widely held belief that the killing was carried out by a friendly country's intelligence agency, namely Mossad.
Experts say arresting Israeli agents - or even digging up further evidence that Israel was involved - could be politically costly.