Sources said the nine-time Lok Sabha MP and former Meghalaya chief minister, whose National People's Party is part of the NDA, held wide-ranging discussions with Shah on the northeast states and sought to expand the NDA base there.
Sangma was NDA's joint candidate for the Presidential poll and was defeated by incumbent Pranab Mukherjee.
He was one of the leaders who formed the Nationalist Congress Party (NCP) headed by Sharad Pawar, after quitting Congress.
He also handed over a memorandum to Modi, who is taking personal interest in development of northeastern region.
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The meeting comes close on the heels of Shah's visit to north-eastern states, where he travelled widely, meeting party workers across states and even addressed public meetings at various places.
BJP is seeking to capture power in north-eastern states, many of which are ruled by Congress and regional parties.
While Assam goes to polls in June 2016, Manipur goes to polls in March 2017 and Meghalaya, Mizoram, Nagaland and Tripura in 2018.