Jain had raised the issue during Zero Hour of the ongoing Monsoon session and quoting the comments, contended that they had hurt the sentiments of Jains.
She alleged that both Dadlani and Congressman Tehsin Poonawala had commented against the monk.
A case was registered against the two at Ambala for allegedly hurting the religious sentiments of the Jain community.
The BJP government in Haryana had invited Sagar to deliver a lecture, 'Kadve Vachan', in the Assembly on the opening day of the session on Friday.
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But now, what Dadlani has said about him, I feel it is an insult to the Assembly and therefore, we should pass a condemnation resolution unanimously," Jain told the House.
After this, she said she was moving the resolution.
However, Leader of Opposition and senior INLD leader Abhay Singh Chautala interrupted saying, "Who has said what about whom, how is that connected to this House."
Congress' Karan Singh Dalal said, "I do not want to state anything as a Congress member on the proposed resolution, but in my personal capacity, I would say we should not involve such saints by making them a part of a House discussion.
Dalal said after Sagar's address, requests were pouring in from Dalit and Sikh saints as well that they too should be allowed to address the House in the future.
Haryana Parliamentary Affairs Minister Ram Bilas Sharma said the House was "unanimous" on the resolution.
However, Chautala said there was no unanimity on it. "It (unanimity) was only limited to inviting the monk and listening to his pravachan (sermon)," he said.
Chautala again contended that the matter did not pertain to the House and it should not be involved in the controversy.
Sensing that the opposition would not back the resolution, Chief Minister Manohar Lal Khattar told the House that a case was registered at Ambala in connection with the remarks and action, as per the law, will follow.
Earlier in the day, Delhi PWD Minister and AAP leader Satyendar Jain met the monk here.
The meeting took place even as Jains staged a protest outside Delhi Chief Minister Arvind Kejriwal's residence in the national capital, demanding immediate arrest of Dadlani, an AAP supporter.
He said the music composer had realised his mistake and was deeply hurt over the issue.
A separate delegation, led by former BJP MP Satya Pal Jain, met Haryana Governor Kaptan Singh Solanki here regarding the matter.
Dadlani had subsequently deleted the controversial tweet and tendered an apology, saying he had made a mistake by offending the peaceful Jains.
He had also apologised to the Jain monk on Twitter.