The parties also demanded that an FIR should be lodged against the minister for her "uncultured" comments.
"The Prime Minister appeared in the House after a long time. He was sitting there, he could have got up and expressed regret on this issue and condemned it," senior Congress leader Kamal Nath told reporters outside Parliament.
He maintained that the statement of the minister has "hurt" the sentiments of secular minded people.
Samajwadi Party leader and Rajya Sabha MP Ram Gopal Yadav said there should be "nothing less than resignation" on the issue.
Also Read
"I am amazed at the statement of the government that the comments by the minister were made outside the House, but the issues we discuss the house are related to people's interest.
"Unless the Prime Minister assures us that he will take action against her, we will not stay quite," Congress leader and Rajya Sabha MP Ashwani Kumar said.
"The offence is non-compoundable and non-bailable. Till the time the minister does not resign, we will not allow the House to function," he said.
Jyoti had yesterday stoked a controversy by allegedly making communal remarks and using an expletive in an election rally here, leaving the BJP and the government embarrassed.