Schulz's remarks, speculating on the result of Sunday's Greek bailout referendum infuriated MEPs within the European parliament's leftist groups after he was reported as saying that his trust in the country's prime minister Alexis Tsipras and his left-wing Syriza party had reached "rock bottom".
In an interview published in the German Handelsblatt business daily on Friday, just two days before the yes/no referendum, Schulz said he hoped that a Tsipras defeat would, "be bridged by a [transitional] technocratic government, so that we can continue to negotiate."
He added, "If this transitional government reaches a reasonable agreement with the creditors, then Syriza's time would be over."
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Syriza party MEP Dimitris Papadimoulis called Schulz's comments "interfering and unacceptable" and accused the German socialist of "ignoring the democratic will of the Greek population".
"He wants to see the democratically elected government overthrown, so that the creditors get a government that suits them," said Papadimoulis in a statement alongside his European United Left/Nordic Green Left group colleague Gabi Zimmer.
"These remarks illustrate how Martin Schulz as president of the only democratically elected EU institution sees democracy […] Schulz is trying to scare the Greek voters that they would be leaving the eurozone and to discredit the Greek government."
As the titular head of the European parliament, Schulz is the institution's public face and official representative. And although the duties are largely ceremonial, how the parliament's president interprets their role often depends to a large extent on their personality, experience and their vision of the role within the EU institutional framework.
Schulz has been criticised on numerous occasions for allegedly overstepping his mark as parliament president, most recently when he was quoted as saying, "Greeks get on my nerves,” following an outburst highlighting his and other EU leaders frustration with Tsipras' negotiation tactics.
Greens/European Free Alliance group co-presidents Rebecca Harms and Philippe Lamberts said they would look to "deal" with Schulz's "totally inappropriate" comments and his position as president of the European parliament during this week's plenary session in Strasbourg.
"We were stunned by Schulz's statements in his interview with Handelsblatt," said the pair, adding, "the remarks speculating on the outcome of the referendum, hoping for a victory of the 'yes' option followed by prime minister Tsipras' resignation and potential replacement of the democratically legitimate Greek government by one run by technocrats is totally inappropriate."
"Regardless of Schulz's commitment to EU integration and his contributions to finding a solution to the Greek crisis and while we recognise the legitimate frustrations that may have been caused by the attitudes of the stakeholders involved, there can be no justification for the statements in this interview."
"This is all the more so given [his] position as president of the European parliament."
Schulz, however, hit back at his accusers. Tweeting that there had been a, "gross misinterpretation that I am wishing for a technocratic government in Greece".
And responding to Sunday's 'no' result, he said that it was important that the democratic will of Greece's voters should be respected, but warned that Tsipras' promises that that a 'no' would improve Greece's negotiating position was, "in my eyes, not true".
"The finance minister's promise that the banks will open tomorrow [Monday] and that money will be available for tomorrow and Tuesday seems to me very difficult and dangerous", he said.
Schulz also suggested that eurozone leaders should consider the possibility of delivering a humanitarian aid programme for Greece when they meet in Brussels on Tuesday.