Draghi was appearing before parliament's economic and monetary affairs (ECON) committee in the bank's first monetary dialogue since November.
Since the ECB president's last appearance before the ECON committee, Lithuania has become the 19th member of the eurozone, the ECB has announced and launched a €60bn asset purchase programme to buy public sector securities, also known as quantitative easing (QE), the ECB inaugurated a new headquarters, and the minutes of a ECB governing council meeting have been published for the first time.
"ECB policy is helping some and suffocating others" - Marisa Matias, GUE/NGL
The ECB chief told MEPs that "the economic recovery in the euro area has clearly strengthened". He attributed this to the fall in oil prices, higher external demand, better financing conditions, and the depreciation of the euro.
Draghi cautioned that the positive results of QE "should not distract [member states] from delivering their contribution to put the economy back on track". He added that, "structural reforms should be implemented promptly and with determination ".
The ECB president predicted that inflation will remain low or negative this year but it will increase gradually later this year. The bank's policy is to "ensure that inflation does not remain too low for too long".
The economic dialogue was dominated by questions from MEPs on the policy of the central bank towards Greece. Athens is currently trying to negotiate a financial assistance package to reduce the risk of insolvency.
In response to EPP ECON member Burkhard Balz, Draghi said, "To have a credible perspective, Greece needs to put in place a process to restore policy dialogue between the Greek government and the three institutions [the ECB, European commission and international monetary fund (IMF)]."
He also reminded S&D ECON member Jakob von Weizsäcker, that "The ECB is a rules-based institution and we are not creating rules for Greece, we are implementing them".
Draghi told the committee that the ECB and IMF teams will return to Athens in September, "something that was unthinkable in February".
Under questioning from the ECR group's Sander Loones, an ECON committee vice-chair, Draghi refused to comment on German media reports that the ECB is developing a number of strategies in the event of a 'Grexit'.
GUE/NGL ECON member Marisa Matias meanwhile accused Draghi of "blackmailing" Greece and said, "ECB policy is helping some and suffocating others".
The Portuguese deputy added that if current policies continue, it will be "unsustainable to have Greece in the eurozone".
Draghi strongly rejected Matias' comments and noted the exposure of the ECB to Greece is €104bn, or 65 per cent of Greek GDP ,and asked, "what kind of blackmail is this?"
Matias also raised the issue of the ECB's new headquarters in Frankfurt. 350 people were arrested in the German city as police clashed with anti-austerity protestors.
In reference to the opening of the €1bn building, originally expected to cost €850m, the GUE/NGL deputy noted, it is "easier [for Draghi] to talk about other people's overspending".
The ECB president also informed MEPS, "the outlooks for 2015 and 2016 have been revised upwards by 0.5 per cent and 0.4 per cent - and inflation is expected to gradually increase from zero per cent in 2015 to 1.8 per cent in 2017".
However, he added these projections were based on "full implementation" of the bank's QE programme.