Senior party spokesperson Anand Sharma said there should be no politics over the issue and the matter be treated as humanitarian.
"The government must immediately call a meeting of leaders of all parties and should inform about the steps it proposes to take," he said, adding that it would be proper if the meeting is called tomorrow.
He said till all matters related to the NRC are disposed, people and families should not be separated or taken to any camp and the matters be kept in abeyance.
The NRC issue is of international importance as it affects relation with neighbouring countries, including Bangladesh. It also has inter and intra state repercussions as well, Sharma said.
The Congress leader said indigenous people and tea plantation labourers have been affected in large numbers.
The government has given the list of 16 documents for identity purposes and any of the 16 would establish the citizenship of the applicant or otherwise, but an overwhelming majority of people are excluded even after giving documents, Sharma said.
"The question arises about the methodology, the efficiency as well as the credibility of the entire process of the exercise," he said.
Sharma also asked whether the government of India has taken up this matter or presented the matter correctly as the Government of the Union should do before the Supreme Court.
Gandhi, in a Facebook post, has also asked Congress members to help maintain peace and help those, irrespective of their caste, religion or group, against whom "injustice" was done in the draft NRC.
The Congress chief said the NRC was initiated by the UPA under Manmohan Singh to fulfil the commitment made in the Assam Accord of 1985.
"However, the manner in which this exercise has been undertaken by the BJP governments at the centre and in Assam leaves much to be desired," he said.
"There are reports pouring in from all corners of Assam of Indian citizens finding their names missing in the draft NRC, creating massive insecurity in the state.
"Clearly, after spending close to Rs 1,200 crore, the execution of this critical and highly sensitive exercise has been tardy. The Government must move swiftly to resolve this crisis," Gandhi said.
Congress spokesperson Sharma said the issue has inter-state dimensions and repercussions and a humanitarian crisis aspect.
"This is not an issue on which politics should be played. That is what we would advise and request the ruling party, which is in government in that state (Assam) and also in Tripura," he said.
He also urged the government to remove shortcomings in the entire process and that all issues be settled as per the 1985 Assam Accord signed in the presence former prime minister Rajiv Gandhi.
The problems should sorted out in the ambit of the Assam Accord of 1985, the Congress leader said.
A massive Supreme Court-monitored exercise to identify genuine Indian nationals living in Assam today excluded over 40 lakh people from the final draft list, triggering a political slugfest with the opposition alleging that it was the BJP's "gameplan" to divide the people for electoral gains.
The issue rocked both house of Parliament after which Home Minister Rajnath Singh appealed to the opposition not to politicise the "sensitive" matter as the list has been published on the directives of the Supreme Court and the Centre has "no role" in it.
Singh asserted that no "coercive" action will be taken against those whose names were excluded from the NRC draft list.
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