They were reacting to Rawat's remarks made at a health summit on Thursday.
"Leaders are not those who lead people in inappropriate directions, as we are witnessing in a large number of university and college students, the way they are leading masses of crowds to carry out arson and violence in our cities and towns. This is not leadership," the Army Chief had said.
After Rawat's remarks triggered a storm, Army had issued a clarification, saying the Army Chief has not referred to the CAA.
"He has not referred to any political event, personality. He was addressing the future citizens of India who are students. (It is his) righteous duty to guide students on whom shall depend the future of the Nation. In Kashmir valley, youths were misguided the first, by people whom they trusted as leaders," the Army statement said.
However, Chidambaram was critical of Rawat's remarks.
"Now, the Army General is being asked to speak up. Is it the job of the Army General? The DGP... the Army General are being asked to support the government. It is a shame. Let me appeal to General Rawat.... You head the Army and mind your business... what politicians will do, politicians will do," the former union minister said.
"It is not the business of the Army to tell politicians what we should do. Just as it is not our business to tell you how to fight a war. You fight war according to your ideas and we will manage the politics of the country," he said.
He was speaking at a rally against the new Act organised by Kerala Pradesh Congress Committee (KPCC) in front of Raj Bhavan in Thiruvananthapuram. Taking strong exception to Rawat's comments on "domestic politics", Yechury said that it had happened "for the first time in independent India".
"This is politicisation happening (in) armed forces. A dangerous trend.. If it continues, ours will also deteriorate, like the role of Army in Pakistan," the Left leader told reporters in Hyderabad.
It is necessary for the country and the Constitution to consider the "warning," he said and appealed to the government to keep it in consideration.
"But, ministers, government have given statements in (news) papers that our Army Chief has done nothing wrong and not interfered (in domestic issues)," the CPI(M) General Secretary said.
Rawat's comments have evoked sharp reactions from opposition leaders, activists and military veterans who accused him of compromising the long-held convention in the Army of not wading into political matters.
Gen Rawat, who is due to retire on December 31 as Army Chief, is tipped to be India's first Chief of Defence Staff who will be the single-point military adviser to the government on tri-services matters.
Former Navy Chief Admiral L Ramdas had said Gen Rawat was "wrong" in making such remarks as people in the armed forces must follow the decades-old principle of serving the country and not any political force.
"The rule is very clear that we are serving the country and not political forces, and to express any political views as we have heard today are quite a wrong thing for any serving personnel whether he is the top gun or at the bottom rank. It is not proper," Ramdas said.
Section 21 of the Army Act prohibits any Army personnel to attend or address any meeting or to take part in any demonstration organised by anybody for any political or other purposes. It also bars them from communicating to press or to publish any book relating to any political question.
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