By Praveen Paramasivam

CHENNAI (Reuters) - A group of more than 1,000 striking workers at the Samsung Electronics factory in southern India has rejected a settlement offer made by the company on wage hikes, with the sit-in protest entering its second month on Wednesday.

The strike is the biggest such labour dispute in recent years in India and has cast a shadow over Prime Minister Narendra Modi's drive to lure investors to set up local manufacturing. Tamil Nadu state, where many foreign companies including Foxconn operate, has been unsuccessful in resolving the matter so far.

The strikers have disrupted production and protested in a makeshift tent close to the factory near the city of Chennai in Tamil Nadu since Sept. 9, demanding higher wages and union recognition. The plant is critical to Samsung's ambitions and accounted for roughly one-fifth of its $12 billion India sales in 2022-23.

Samsung this week made a proposal to provide a monthly incentive of 5,000 rupees ($60) until March, more air conditioned buses, a diversified cafeteria menu and a gift card of $24 in case of a child birth, according to the settlement document seen by Reuters.

But the labour group backing the protests, the Centre of Indian Trade Unions (CITU), has rejected the agreement as it doesn't recognise their union, A. Soundararajan, its state president said on Wednesday.

"We will continue striking. We will intensify our protest to put pressure on the government," he told Reuters.

Samsung said in a statement it signed an agreement and will engage with workers to address their concerns, but it did not comment on the strike still continuing.

State industries minister T.R.B. Rajaa said on Tuesday Samsung had agreed to fulfil 14 demands and was willing to discuss more, but the "workers should return to work" and all their demands, including union recognition, will be considered.

Samsung workers earn 25,000 rupees ($300) on average each month and are demanding a raise of 36,000 rupees a month spread over three years, according to the CITU. Samsung has said the average monthly salary of full-time manufacturing workers at the plant is nearly double that of similar workers in the region.

The plant, which employs roughly 1,800 permanent workers and makes refrigerators, TVs and washing machines, is one of Samsung's two factories in India. The other one in Uttar Pradesh state makes smartphones, but has witnessed no labour unrest.

(Reporting by Praveen Paramasivam; Editing by Aditya Kalra ad Raju Gopalakrishnan)