"Any threat received by anyone against the prime minister, howsoever suspicious the threat is, howsoever vague, even if it is a rumour, it should be taken seriously. Action should be taken, investigations should be done," party spokesperson Pawan Khera told reporters.
Lashing out at elements "attempting to politicise the issue", he said "do not use a threat to the PM of India for petty politics".
"We have lost two prime ministers. We have lost an entire leadership in the Chhattisgarh violence. We know what it means to fight terrorism, to fight naxalism. But do not play politics. We lost leadership in Chhattisgarh when the BJP was in power. Did we play politics in Chhattisgarh, we did not," he said, while replying to a question.
Maharashtra Congress also today said the state government and the Centre should make a statement on the alleged Maoist threats to Prime Minister Narendra Modi and Chief Minister Devendra Fadnavis.
The police in Pune on Thursday told a court that they had seized a "letter" from the Delhi residence of one of the five people arrested on Wednesday for having alleged "links" with the banned CPI (Maoist).
Mr Khera also criticised "attempts at politicising" the Bhima-Koregaon violence and said the BJP government was "exposed" in the matter when Union minister Ramdas Athawale challenged their own government in Maharashtra and the police saying that there was no relation of Elgaar Parishad with the violence.
Mr Athawale had also called the arrests of Dalit activists in connection with the violence as injustice.
The Congress spokesperson said that during the UPA 2, the government faced a lot of dissent but it never labelled dissenting voices as anti-nationals.
He said the government should face dissent with facts.