Chief Minister Conrad K Sangma had said his party will decide on the future course of action.
The Meghalaya Democratic Alliance cabinet, which has two Bharatiya Janata Party (BJP) ministers, has passed a resolution opposing the Citizenship (Amendment) Bill.
The BJP leadership in the state asserted they were "with the indigenous people" on the proposed legislation.
The Cabinet passed the resolution during a meeting on Thursday.
The BJP, which has two MLAs in the MDA government, backed the Cabinet decision.
"We are with the people of the state. The state cabinet had unanimously passed a resolution to oppose the Bill and we are part of the government," Health Minister and BJP MLA AL Hek said.
Asked if he would resign from the BJP on the issue, he said: "No question."
"People have voted for me. They have entrusted me with responsibilities as their representative and I will continue to serve in that capacity," he added.
The ruling National People''s Party (NPP), the United Democratic Party (UDP), the BJP and the Hills State Peoples Democratic Party, as well as the opposition Congress, have voiced their opposition to the Bill, reflecting strong dissent prevailing in the state against the proposed legislation, cleared by the Lok Sabha.
The ruling UDP (having nine MLAs) has aired its opposition to the Bill and party president Donkupar Roy slammed the BJP at the Centre for "going against the voices of the people", particularly in the frontier states of the northeast region.
Mr Roy, who is also the speaker of the Meghalaya Legislative Assembly, said: "There is a great danger in accepting the Bill in its current form, and if it's implemented in the frontier states of the North East, particularly in Meghalaya... the Bill would open the gates for illegal immigrants from Bangladesh to come into the state and in the northeast. We do not want the indigenous population to become a minority in our own state."
The speaker demanded the state and the northeast region be exempt from implementing the proposed legislation "going by the sentiments of the indigenous people."
National Peoples Party (NPP) president and Chief Minister Conrad K Sangma had said his party will be meeting in the coming days to decide on the future course of action of the party with regards to the Citizenship Bill. The NPP is heading the MDA government and has 20 lawmakers in the 60-member House.
The Hills State Peoples Democratic Party (with 2 MLAs), and part of the ruling MDA government, wrote to Prime Minister Narendra Modi on Thursday demanding reconsideration of the implementation of the Bill, party lawmaker Renikton said.