Mr Bansal got furious when a journalist asked him about the companies owned by his family.
"Shall I call you in separately and explain the definition of family?" Mr Bansal hit back. He was interacting with the media briefly after his arrival in the city.
Following this, the Chandigarh Press Club issued a statement, objecting to the remarks made by Mr Bansal, who is the MP from Chandigarh.
"He (media person) has virtually been threatened by Pawan Kumar Bansal at his residence in Chandigarh. The Chandigarh Press Club has taken a serious note of this and it is highly unbecoming of a person of Mr Bansal's stature to intimidate a journalist on duty. The press club demands an unconditional apology from Mr Bansal," the statement said.
Bharatiya Janata Party (BJP) leader Satya Pal Jain also sought an "unqualified apology" from Mr Bansal, while criticising the "highly derogatory and threatening language" used by the former Railway Minister.
"Bansal himself is responsible for whatever has come in the media during the last few days about the railways job scam and the situation in which the former railway minister finds himself today," he said.
Leaders of the Congress had gathered at Mr Bansal's residence to show solidarity with him. He told party leaders that he had nothing to do with the bribery scam involving his relatives.
Mr Bansal drove into Chandigarh from New Delhi on Saturday with virtually no leaders and relatives being present at his house to receive him.
He was forced to quit as Railway Minister on Friday after a bribery controversy surrounding his nephew Vijay Singla.
The Central Bureau of Investigation (CBI) arrested Mr Singla on May 3 and recovered Rs.90 lakh from him which was allegedly paid to him by a senior railway officer to get a lucrative posting. This was followed by other allegations that Mr Bansal allegedly used his official status to benefit close relatives and associates.