Union minister Prakash Javadekar also asked the Congress and its former president Sonia Gandhi to make their stand clear on the issue of illegal Bangladeshi immigrants in the country.
The TMC, he told a press conference, was nervous due to growing strength of the BJP in West Bengal.
Union Minister Ravi Shankar Prasad said it was a new low for parliamentary democracy that opposition members did not allow Shah to speak. "This is a new precedent and a new low," he told reporters.
Javadekar hit out at the opposition after its members began protesting when Shah rose to speak in the Rajya Sabha, forcing its adjournment for the day.
They had created a ruckus on Tuesday as well when Shah said that the BJP government had to the courage to implement the Supreme Court's decision on the NRC while the previous Congress dispensations lacked it.
"They deliberately raised objections to prevent Shah from completing his speech. It is murder of democracy to prevent a member of the House from speaking," Javadekar told reporters.
The Assam Accord to identify illegal immigrants was designed by then prime minister and Congress leader Rajiv Gandhi, he said, adding that Shah only asserted that the BJP was implementing the NRC, which was the "soul" of the accord.
Javadekar claimed even Indira Gandhi had said that the Bangladeshis should return to their country after the situation there normalised following the Indo-Pak war in 1971.
"We now want to ask about the stand of Sonia Gandhi on the NRC and on evicting infiltrators from the country," the minister said.
Javadekar also condemned TMC supremo Mamta Banerjee's reported statement that exclusion of over 40 lakh people from the NRC in Assam would lead to "civil war".
He also asserted that Shah would participate in a Kolkata rally on August 11, saying the local police had not done any favour to the BJP by granting permission to it.