The party did not respond to the Speaker's invitation to a group photo session with the governor, whose speech on the first day of the session was disrupted by the opposition.
Congress MLA Abdul Khaleque alleged that attempts were being made to "safronise the Assembly and the colours of only one party's flag were used to decorate the premises".
"We are boycotting the photo session and the tea party in protest," he said.
Responding to the allegation, Assam Assembly Speaker Hitendra Nath Goswami said in the House: "I did not know about this. When I reached home last night, I saw it on TV. Then immediately I asked to remove it as we did not want to hurt anyone."
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The Budget Session will conclude on April 6.
Later, at a press conference in the Assembly complex, Leader of the Opposition Debabrata Saikia said the Assembly is above party politics and it is unfortunate that the government wanted to spread its "ill motives" by neglecting the Speaker.
"But this time, they made arrangements for MLAs and senior bureaucrats in the Central Hall, while journalists and other people were served tea outside in the open. This is discriminatory. We boycotted the tea party for this also," he added.
Former Chief Minister Tarun Gogoi said journalists are an integral part of democracy and they have always been functioning together with the members of the House.
"The government is run by the RSS, not by the chief minister or Himanta (Biswa Sarma). It is a matter of big concern that they (RSS) are now trying to capture the Assembly," Gogoi alleged at the press conference.
Senior Congress MLA Rakibul Hussain said the All India United Democratic Front accepted the tea party invitation and went ahead with the photo session, showing that "they support saffronisation".