India will not invite Pakistan Prime Minister Imran Khan to Thursday's swearing-in ceremony of Narendra Modi, who starts his second term as India's prime minister, two sources in the foreign ministry said, suggesting any early warming in ties between the nuclear-armed neighbours is unlikely.

Hindu-majority India and Muslim-majority Pakistan have fought three wars since both won independence from Britain in 1947, and came close to a fourth in February after a suicide attack by a Pakistan-based militant group killed at least 40 Indian police in the contested Kashmir region.

An Indian government statement on Monday said the leaders of Bangladesh, Myanmar, Sri Lanka, Thailand, Nepal, and Bhutan - all members, with India, of the little-known Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC) - have been invited to Modi's swearing-in.

"This is in line with Government's focus on its 'Neighbourhood First' policy," a government spokesman said.

The leaders of Kyrgyzstan and Mauritius have also been invited, but two sources in Indian's foreign ministry said Pakistan will not be on the list, without providing further information.

For the swearing-in ceremony for Modi's first term in 2014, all nations from the South Asian Association for Regional Cooperation (SAARC), that includes Afghanistan, Pakistan and the Maldives, were invited.

In 2014 Pakistan's then-Prime Minister Nawaz Sharif attended the ceremony, to the anger of some of Modi's Hindu-nationalist allies.

Modi and Khan both claimed their air forces carried out air strikes in enemy territory in March, to the alarm of world powers.

Modi, who was widely believed to have benefited politically from the stand-off, won a second term with an increased majority in a general election whose results were declared last week.

Khan called Modi on Sunday to congratulate him on his win.

Modi could still meet Khan at a Shanghai Cooperation Organization summit in Kyrgyzstan next month, that both leaders may attend.