Members of the Hindu United Front have vowed to walk to the port in Vizhinjam, on the southern tip of India, to pledge their support for a project they say will create jobs in the region.
Construction has been halted for almost four months by protesters from a fishing community who say the port is causing erosion that has hit their livelihoods.
The villagers, led by Catholic priests, are blocking the site's entrance with a makeshift shelter, and an attempt by police to intervene triggered clashes which injured more than 80 people.
In a bid to stave off fresh violence, a senior police officer said even more security had been deployed around the port to prevent the Hindu group from reaching it.
"We have denied permission to the rally by the Hindu United Front. We have taken enough precautions to prevent it if the front defy the order," Trivandrum Deputy Commissioner of Police Ajith V told Reuters.
The port is of strategic importance to both India and billionaire Gautam Adani, Asia's wealthiest man and the world's third-richest. Once completed, it will become India's first container transhipment hub, rivalling Dubai, Singapore and Sri Lanka for business on the lucrative east-west trade routes.
Critics say Adani, who comes from the same state as Modi, has benefited from the policies of the federal government.
Both Adani's conglomerate and the government of Kerala have denied accusations the port is causing environmental damage.
Supporters of the port have set up their own shelter across the street from the protesters. Earlier, Hindu United Front member C Babu told Reuters they would go ahead with the rally.
Kerala state police have already sent reinforcements to the Vizhinjam area after villagers stormed a police station late Sunday in clashes.
The protest has continued despite repeated orders by Kerala's top court to allow construction to restart. However, police have so far been unwilling to take action, fearful that doing so will set off social and religious tensions.
The first phase of construction was due to be completed by end-2024. The Adani Group has said in court filings that the protests have caused "immense loss" and "considerable delay".
Adani has also faced protests in Australia, where environmental activists had launched a "Stop Adani" movement to protest his Carmichael coal mine project in Queensland state.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.
