Delhi Journalist Association (DJA), an affiliate of National Union of Journalists, asked the Congress party to "express regret" and "apologise" in keeping with its "long and brilliant past".
In a statement issued here, the DJA said, "badmouthing a journalist simply because she conducted an interview with a rival political leader is in poor taste and amounts to shooting the messenger."
It described Gandhi's comments made yesterday as "unwarranted and unbecoming of a senior leader of a national political party."
The Press Club of India, Indian Women's Press Corps and Press Association issued a joint statement separately, saying the media expects "restraint from political class" at large while commenting on them.
"We the undersigned organizations express concern over the gradual decline in nature of political discourse, more so in a highly polarized political environment," the three organisations said.
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"Terms like 'presstitute' used by a former union minister and more recently 'pliable' by the president of a political party for the media are inappropriate and lower the dignity of discourse in general," they added.
These organisations urged all sections of civil society including sections of political leadership cutting across all political parties to be temperate in their criticism towards each other as well as towards the Indian media.
"While journalists are expected of neutrality, we, as media, too expect restraint from political class at large while commenting on them especially when the political atmosphere is getting charged in view of the coming general elections in the country," the joint statement said.
They also expressed deep concern over the continued incarceration of Manipur journalist Kishorechand Wangkhem under the National Security Act for his social media post criticising members of the ruling party at the state and centre.
"We reiterate our demand that the charges against Mr Wangkhem be dropped, more so after he was exonerated earlier by a court that did not find anything seditious in his remarks," they added.
The DJA said it was "not amused at use of adjective 'pliable' by Indian National Congress President Rahul Gandhi for the ANI interviewer who conducted a wide-ranging and long interview with Prime Minister Narendra Modi."
It said it is "of the opinion that journalists have a professional responsibility to seek information, ask questions and get answers.
"All journalists everywhere know that making your interview subject uneasy is not the best strategy and turning an interview into interrogation or inquisition may dry the information channels and thus become counter-productive," the statement said.
The DJA said that many Congress stalwarts were journalists and they knew media ethics.
"We expect the party to reiterate its respect for the freedom and dignity of the press," said the statement.