That includes BJP loyalists Rajnath Singh, Amit Shah, Nitin Gadkari, Nirmala Sitharaman and S.Jaishankar – the defence, interior, transport, finance and foreign ministers respectively, staying on in their jobs.
Powerful BJP president Jagat Prakash Nadda was named as health minister.
Posts given to coalition leaders include civil aviation, to Kinjarapu Rammohan Naidu of the Telugu Desam Party (TDP), the BJP’s biggest ally.
Other coalition posts include smaller ministries such as heavy industry, food processing and fisheries.
There are no Muslim lawmakers among his third-term lineup, unlike his past two governments, both formed after his right-wing BJP won a majority.
Modi’s decade as premier has seen him cultivate an image as an aggressive champion of the country’s majority Hindu faith, worrying minorities including the country’s 200-million-plus Muslim community.
“Honoured to serve Bharat”, Modi wrote after he was sworn into office, using the country’s name in Sanskrit, a word dating back to ancient Hindu scriptures.
He held his first cabinet meeting Monday evening, where plans were approved for assistance for 30 million new homes for poor families.
Modi had been forced into quick-fire talks with coalition partners in the National Democratic Alliance (NDA), whose 293 seats guaranteed him the parliamentary numbers to govern.
Earlier on Monday, Modi took his first action, approving the latest tranche of a cash handout for 93 million farmers.
Two-thirds of India’s 1.4 billion people draw their livelihood from agriculture, which accounts for nearly a fifth of the country’s gross domestic product.
Despite the BJP dominance in the cabinet, the coalition means Modi must seek greater consensus in this parliament.
The TDP from Andhra Pradesh is led by veteran politician Chandrababu Naidu, who began his political career with Congress, the biggest opposition party to the BJP.
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Modi’s BJP claims ‘historic’ victory in Indian election despite smaller majority
Modi’s BJP claims ‘historic’ victory in Indian election despite smaller majority
The next biggest, the Janata Dal (United) party of Bihar, is headed by Nitish Kumar, who has a history of frequently changing his allegiance to and from the BJP to suit his interests.
He was one of the founding members of the opposition alliance that competed against Modi in this year’s election – but switched sides just weeks before the vote began.
Seven of the 71 ministers are women, with two in the top cabinet.
Modi’s chief rival Rahul Gandhi was nominated on Saturday to lead India’s opposition in parliament, after he defied forecasts to help the Congress party nearly double its seats.
No date has been set for the opening of parliament, but Indian media have reported the new session is expected to begin next week, when the speaker will be elected.