Members of the opposition BJP boycotted the meeting of the AAP-led municipal House on Thursday while a Congress woman councillor objected to the session being called on the last day of the month and on the occasion of Raksha Bandhan.
Delhi Mayor Shelly Oberoi during the House said "we celebrate our festivals, but we also know our duties".
She took a jibe at the BJP and said "people cannot run away from their responsibilities in the name of a festival".
She also asserted that the opposition should not try to give it a political colour.
An AAP member said the BJP councillors not attending the meeting of the House "was a matter of shame" as he accused them of shying away from their duties in the name of Raksha Bandhan.
The Delhi BJP on August 29 had announced that if the House was held on the day of Raksha Bandhan, its members will not attend it and alleged that it amounted to "harassment" of municipal employees.
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The festival this year has fallen on both August 30 and 31.
"If the Aam Aadmi Party holds the meeting of the municipal House on the day of Raksha Bandhan, then the BJP councillors will boycott the meeting," Delhi BJP's general secretary Kamaljit Sehrawat said at a press conference earlier.
On August 29, she had told reporters that the House has been called on August 31, the last day of the month, which is the day of Raksha Bandhan and "we strongly condemn it".
On Thursday, Congress councillor Naziya Danish vehemently objected to the House being held on the day of Raksha Bandhan. Leader of House Mukesh Goyal countered that a government holiday for the occasion was on August 30.
"The House should not have been called on the day of Raksha Bandhan, this is wrong," she charged.
Delhi Mayor Oberoi later at a press conference after the House meeting said it was unfortunate that BJP members did not attend the session, adding they should not try to give it a political colour.
When asked about weekly reports on cases of vector-borne diseases not being released by the MCD in the past two weeks, she said, "I will speak to the officials on this matter."
The House passed a slew of proposals including exponentially raising the quantum of a councillor's allowance from Rs 300 to Rs 25,000 per meeting, a move that has drawn criticism from the opposition BJP.