"We hope other political groups including UPA and NDA will respond to the call of conscience by the tribal people," he told reporters here, reiterating that India had not had a president from the tribal community.
But apart from the AIADMK and the Biju Janata Dal (BJD), who jointly proposed his candidature May 17, no other party has responded favourably to him.
Sangma Tuesday met Sitaram Yechury and Prakash Karat of the Communist Party of India-Marxist (CPI-M) as well as Arun Jaitley and Sushma Swaraj of the Bharatiya Janata Party (BJP) to plead his case.
He has also sought a meeting with Congress president Sonia Gandhi, whom he had dubbed a "foreigner" in 1999 when he walked out of the Congress party.
The Congress, BJP and Left have not yet backed Sangma. Sources in all three parties indicate that he is not their preferred choice for the top job.
Sangma's Nationalist Congress Party (NCP) has said it will go with the choice of the Congress-led United Progressive Alliance (UPA), of which it is a constituent.
Sangma's daughter, Minister of State for Rural Development Agatha Sangma, told a news channel that she was hopeful.
"The UPA will take a collective decision and I hope it will be on the positive side," she told Times Now.
On Tuesday, Sangma met Odisha Chief Minister Naveen Patnaik here and then issued a call to political parties to join the "common cause of projecting a tribal as a presidential candidate".
Patnaik praised Sangma as the most suitable candidate for the job -- words used by his Tamil Nadu counterpart J. Jayalalithaa earlier.
"I was so happy Patnaikjii responded firstly, and then, Jayalalithaaji also. On behalf of myself, on behalf of the entire tribal population of the country, I would like to express my gratitude," Sangma said.
Patnaik and Jayalalithaa, who are known to enjoy a good rapport, sprang a surprise last week by announcing their joint support for Sangma.
President Pratibha Patil's term ends July 25.
Meanwhile, the Election Commission has begun preparatory meetings for holding the presidential elections.
Until Sangma's name cropped up, the only people who were being widely talked about as likely candidates were Vice President Hamid Ansari and Finance Minister Pranab Mukherjee.
West Bengal Chief Minister and Trinamool Congress chief Mamata Banerjee has, however, come out against Mukherjee.
She said she will prefer Lok Sabha Meira Kumar, Gopal Gandhi or former president A.P.J. Abdul Kalam as the next president, not Mukherjee.