Condemning the episode, the JD(U), which has been supporting the students, termed the alleged threats to Yechury as an "attack" on the freedom of speech and likened the developments to a "new kind" of Emergency.
"All this (threat calls), we are prepared to face, we are not worried. We are not worried about being labelled as anti-national. We are prepared to face this and we will fight it out," CPI(M) leader Prakash Karat said.
"So, obviously, those forces are angry with us and this is what they try to do at our office," he added.
CPI national secretary D Raja, who too had claimed to have received similar calls over his support to the protesters, said the parties will take up the issue formally with the government now.
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"I do get threat calls. When we met the Home Minister, I did raise the issue with him that we are getting anonymous calls, threatening to shoot us down. All these things are happening. So, we will be taking it up formally with the government," Raja added.
"This is an attack on the freedom of speech, freedom of political parties to function. We had seen such incidents during the Emergency. This is new kind of Emergency we are witnessing," Tyagi said.
The CPI(M) has claimed that Yechury received threat calls for supporting students protesting JNUSU president Kanhaiya Kumar's arrest.