He was asked to appear next week before the European Parliament's money laundering, tax avoidance and tax evasion inquiry committee, which is looking into the scandal, but has declined.
He said he would have no problem facing MEPs, but only after the committee has completed its work.
The committee had requested Muscat to appear before it in Strasbourg from 15-18 May.
The Panama Papers scandal began last year with the leak of 11.5 million documents from the offshore law firm Mossack Fonseca. Malta's EU Council presidency, which began in January, has subsequently been rocked by a series of allegations of money laundering and kickbacks.
The direct allegations against Muscat, which he denies, are the subject of a judicial inquiry opened last month at the Prime Minister's own request.
Muscat has, most recently, faced fresh allegations that a third Panamanian offshore company belongs to his wife. Having an offshore company is not illegal but it is often associated with money laundering schemes.
Muscat denies all the allegations, including that an aide took bribes to secure Maltese passports for wealthy Russians.
Malta has also been accused of being a tax haven. Some companies in the EU's smallest country pay as little as five per cent tax on their profits.
Last month, Malta's left-of-centre government survived a parliamentary no-confidence vote over the Panama Papers scandal.
Earlier this month, Muscat called a snap election for 3 June, nine months before the end of his term.
Reacting to Muscat's refusal to appear before MEPs in Strasbourg, German Greens MEP Sven Giegold said, "I am aware of his public statement that he will not come next week and I expect a hot plenary debate on the matter."
Giegold, financial and economic policy spokesperson of the Greens/EFA group, said, "Muscat has to explain the latest developments and allegations regarding the offshore company called e-grant. The credibility of the EU is at stake, as Malta holds the presidency of the EU and is currently negotiating on revising the anti-money laundering standards. It is also highly unusual to call for elections during a presidency and this election may not delay the inquiry of Parliament.
Committee Chair Werner Langen said, "The PANA-committee expects Muscat to accept our invitation. The cooperation we have received so far from the Maltese Council presidency is disappointing.
"Now that Muscat has called for early elections as a result of allegations that his wife received money into a secret bank account, I hope that, as President-in-Office of the Council, he will use this opportunity to give a public explanation."
Langen added, "Moreover, we see a need for the Maltese government to call for an independent investigation into this matter."
Molly Scott Cato, a Green MEP and also PANA committee member, said, "The latest developments and allegations place at stake the credibility of the EU."
Asked this week by the Maltese press why he would not face the PANA committee on May 18 "if he had nothing to hide", Muscat said he would wait until all the facts were in hand.