The rebel legislators, including two former ministers in Sangma's cabinet, are Frankenstein W Momin, Augustine D Marak, Sayeedullah Nongrum and Samuel Sangma.
"We have submitted a letter to the Congress president expressing our desire to resign from the membership of the assembly over the leadership issue," Momin told a news agency.
Momin said: "We haven't decided when to put in our papers, it will be done at an appropriate time if the (leadership) issue is not resolved."
"We are demanding his (Sangma) removal as we are not happy with his autocratic style of functioning."
In the wake of their threats, Sonia Gandhi has invited Sangma and his political rival Lapang to her 10, Janpath residence on Friday to resolve the issue.
"Madam (Sonia) has invited them with the sole intention of settling group rivalries," a senior Congress leader told the news agency on condition of anonymity.
Sangma June 7 reshuffled his cabinet by sacking four ministers - Prestone Tynsong, Frankenstein W Momin, Augustine D Marak and Founder Strong Cajee - who have demanded his ouster as chief minister.
However, only three Congress legislators - Shitlang Pale, Saleng Sangma and Alexander Hek - were inducted in the cabinet, while SW Rymbai skipped the oathtaking ceremony due to ill-health.
The Congress, which has 28 legislators, enjoys the support of nine United Democratic Party (UDP) members. The Nationalist Congress Party, the main opposition, has 15 members in the 60-seat Assembly.
Meghalaya has seen nine governments with varied combinations, resulting in eight chief ministers between 1998 and 2009. Since Meghalaya attained statehood in 1972, only two chief ministers have completed a full five-year term.
Shillong: Demanding Chief Minister Mukul Sangma's resignation, four Meghalaya Congress legislators have threatened to quit, even as party president Sonia Gandhi meets him and his political rival DD Lapang later on Friday.
First Published: Friday, July 08, 2011, 14:39