Members of five political groups – the Greens, socialists, liberals, European People's Party and European Conservatives and Reformists – signed a petition lobbying the EU assembly's Conference of Presidents, who will decide on 12 May whether to establish the new committee.
The acceptance of World Health Organisation advice by the EU is likely to be at the centre of any probe, as was the case when the Council of Europe launched an investigation into the handling of the flu outbreak.
Governments have been left with excess stocks of vaccines and antiviral medicines worth millions of euro after the expected wave of infections failed to materialise.
Critics claim the threat from the virus was oversold, but the WHO argues that the response to the outbreak was based on the best available information.
The debate has divided experts between those who believe it was better to err on the side of safety, and those who say health resources could have been better spent.
MEPs also want to investigate the role of the European Medicines Agency (EMA) and the European Centre for Prevention and Disease Control (ECDC) to see how decisions were taken.
They are particularly worried by the impact the pandemic will have on public confidence in experts.
French Green MEP Michèle Rivasi said MEPs want to probe whether the experts advising the EU institutions were too close to the pharmaceutical industry.
A committee could also look at the feasibility of a common European approach for buying and distributing vaccines across the EU – something which was lacking during the 2009 outbreak.
