Hridayesh Tripathi of Terai Madhes Democratic Party, Rajendra Shrestha of Federal Democratic Forum Nepal and Ram Naresh Raya, senior leader of Terai Madhes Sadhbhawana Party, are the members of the taskforce.
However, Rajendra Mahato-led Sadbhawana Party, one of the constituents of the four-party United Democratic Madhesi Front (UDMF), has not been included in the panel.
Mahato was injured in a baton charge by police in Biratnagar last week; his party has announced fresh protest programmes, demanding apology for the attack on its chairman.
Madhesis, who share strong cultural and family bonds with Indians, demand a re-demarcation of provinces, fixing of electoral constituencies on the basis of population and proportional representation.
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The major parties have appointed Mahesh Acharya of the Nepali Congress (NC), Bhim Rawal of the CPN-UML and Krishna Bahadur Mahara of the UCPN (Maoist) to the panel.
The Sunday talks were attended by Prime Minister KP Sharma Oli, NC president Sushil Koirala and UCPN-Maoist chairman Prachanda.
So far, over 50 people have died in the Madhesi-Tharu agitation, seeking changes in the constitution.
The Speaker of Nepal's Parliament, Onsari Ghartimagar, yesterday gave a 72-hour deadline to lawmakers to register their amendment proposal on the Bill on First Amendment to the new Constitution, after the discussion on the proposed Constitution Amendment Bill concluded on Sunday.
Speaking at a parliament meeting, Minister for Law, Justice and Parliamentary Affairs Agni Prasad Kharel requested the UDMF to utilise the 72 hours to find a solution and resolve the problems related to the Madhesi community.