As part of a fact-finding mission to the country, MEPs requested a meeting with members of the Maltese Parliament.
The delegation asked to meet with members and former members of the Maltese government but only finance minister Edward Scicluna and Beppe Fenech Adami, the former minister of internal affairs and Nationalist Party deputy leader, have so far confirmed their participation.
Ninu Zammit, former minister of energy, was approached but has not responded to the invitation.
The same applies to Keith Schembri, chief of staff to the Maltese Prime Minister, and Nexia BT, the audit, tax and advisory firm which is reported to have provided senior Maltese government minister Konrad Mizzi and Schembri with services in setting up offshore structures.
Each are said to have had some involvement in the Panama Papers affair and were approached by the parliamentary delegation.
MEPs are investigating the ways in which money laundering, tax evasion and tax avoidance are made possible in the EU. They are also looking at who is responsible, and how these issues can be tackled.
Questions have been asked in particular about the involvement of Malta, current holder of the EU Council presidency, and several of its government ministers, in the Panama Papers scandal.
Attention has focused in particular on the part played in Konrad Mizzi - the only sitting minister in Europe to be named in the scandal last year.
Last April, the Maltese press reported that Mizzi, a senior minister and close ally of Maltese Prime Minister Joseph Muscat, had opened offshore companies and trusts in New Zealand and Panama through Mossack Fonseca, the law firm at the heart of the scandal.
Mizzi's financial advisor also reportedly attempted to open a bank account into which at least €1m was expected to be deposited each year - even though Mizzi's ministerial salary is only a fraction of that. The Maltese opposition has alleged that Mizzi took kickbacks from companies involved in privatisation deals involving several hospitals and the island's power station.
Mizzi has strongly rejected suggestions of any wrongdoing, saying that his "financial affairs have been very clear throughout."
German Greens/EFA MEP Sven Giegold, financial and economic policy spokesperson for his group, condemned the apparent refusal of some ministers to meet the delegation later this month.
On Wednesday, Giegold told this website, "The failure to participate in serious inquiries suggests that there is something to hide. All member states have the duty to cooperate sincerely with inquiries of the European Parliament.
"It should be considered an honour, not a pain, to be invited by the European Parliament. I expect all persons invited to accept our invitation. If countries don't play ball with the inquiry, we need to consider other methods of encouraging cooperation."