The video also showed that the woman minister, Shantana Chakma, trying to move away Deb's hand.
However, both the ministers, who belong to the BJP, have denied allegations by the opposition CPI-M that Chakma was "mishandled".
Chakma, who is the state social welfare minister, told reporters on Tuesday that the incident was being "blown out of proportion by the opposition".
"I did not find any ill motive in the action of Manoj Kanti Deb. He was trying to get a better view of the PM's inauguration ceremony and trying to go to the front. The CPI(M) is trying to politicize the issue for political gain," she said.
"I will file defamation case against the CPI(M) leaders who are spreading canards against me," she told a press conference.
Modi had visited Tripura on Saturday. He had inaugurated a statue of Maharaja Bir Bikram Kishore Manikya Bahadur, the last king of Tripuras Manikya dynasty, at the airport here, addressed a rally and inaugurated two projects.
The CPI(M)'s women wing, All India Democratic Women's Association (AIDWA), held a rally here on Monday demanding the sacking and arrest of Deb, the state's food and civil supply minister for the alleged "mishandling".
AIDWA leaders Rama Das, Krishna Rakshit, Panchali Bhattacharjee and others also demanded that legal action be initiated against him.
When asked, Deb echoing Chakma said the allegations against him were "false and baseless" and was made by the CPI(M) to "derive political mileage".
"I was trying to go in front of Santana Chakma to have a better view of the prime ministers inauguration event. Since she was standing in front of me, I tried to move her aside. That's all," he said.
When asked to comment on Deb's reply, Rama Das, who is also a CPI(M) central committee member, said it was an "endeavour to hide his misdeeds".
"We have noticed that both the ministers have denied the allegation. But the video footage shows everything clearly. When a woman cabinet minister is not safe, I wonder how safe are women in the state," she added.
Demanding an inquiry into the incident, state Congress vice-president Tapas Dey said, "Such incidents should not take place in public life. It is not desirable and should be properly investigated."
BJP spokesperson Ashok Sinha said that the allegations of the CPI(M) and Congress are "politically motivated".
"Now they (opposition) are not getting any political issue, so they are trying to make a non-issue into a issue," he said.
The BJP-IPFT combine had come to power in the state in 2018, ending 25 years of uninterrupted rule of the CPI(M)-led Left Front in Tripura.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)