Express Wi-fi offers software to local entrepreneurs to allow them to work with service providers and share their internet connection with the public for a fee.
Users have access to a variety of services, including news and weather reports.
One critic of Facebook's previous plans was more receptive to this one.
"I think it's a great initiative, we need more companies providing access to the internet in India," said Nikhil Pahwa, editor and publisher of MediaNama, an Indian news site.
"So long as they don't only provide access to certain websites or under certain conditions, then this is a great thing."
Mr Pahwa had previously criticised Facebook's proposal to bring more limited internet access to regions where getting online can be next to impossible. He helped organise the Save the Internet campaign in India.
In February, India's telecoms regulation blocked Facebook's Free Basics internet service app due to the restricted nature of the service provided.
The app offered access to only a limited number of websites.
It was opposed on principles of net neutrality, with protestors arguing that data providers should not favour some online services over others.
The new system makes no mention of limitations on the sites accessible.
"Express Wi-fi empowers local entrepreneurs to help provide quality internet access to their neighbours and make a steady income," its website states.
"India has mobile connectivity but it's never going to meet the demand," said Mr Pahwa.
"In India, you have slow internet and slower internet. There is no such thing as high speed. Mobile access is usually the most expensive sort of internet access, so it's not ideal."
It is likely Indians will still use their mobile devices to access the internet, but by using Express Wi-fi, the hope is that it will be faster and cheaper to do so.
Facebook says it will expand Express Wi-fi to other regions "soon".
The details of the cost of accessing the internet under the scheme and where exactly in India the service is available were not immediately made clear by Facebook.
Facebook has launched a scheme to bring internet access to underserved locations in India.