Meanwhile, coming out in support of party MP Ravindra Gaikwad by calling the airlines ban on him "illogical", the Shiv Sena said that it looks like somebody is trying to defame party leaders.
The problem is all airlines have restricted him.
The controversy erupted in a heated exchange in Parliament before the hint that the government was mulling a way out emerged later in the day.
Though she did not categorically call for the lifting of the ban, she pointed out that MPs need to attend Parliament and they can not always travel by train. They can not come by train every time.
Speaker Sumitra Mahajan told the protesting Shiv Sena MPs that they were not sending a right message.
"I am playing the role of "tai" (elder sister)". It is time to calm down and resolve the issue.
Gaikwad, who represents Osmanabad in Maharashtra, on Thursday repeatedly beat up the Air India official with a slipper after he was made to travel in Economy Class from Pune to Delhi despite holding a Business Class ticket.
The multi-pronged strategy is being considered after the flying ban on Gaikwad was raised in Parliament on Monday. They also demanded that Air India and other airlines should lift the ban on Gaikwad.
"Imposing the ban when the House is in session is not acceptable".
After the meeting, the Speaker said, "Kiski galti hui, kya hua wo alag baat hai". "Violence on a flight can be disastrous. we cannot compromise safety in airlines", Civil Aviation Minister Ashok Gajapathi Raju replied to Sena. "Around November 2014, there was a lot of discussion and a civil aviation requirement was put out by the government which had to do with demeanour of a person", Raju said.
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"Violence of any kind (can) be a disaster". We will talk to our MP, will listen to what he has to say and will see about it.
Raju's response drew applause from some Opposition members who were locked in a verbal duel with Sena MPs.
The proposed move comes in the wake of the controversy involving Shiv Sena member of Parliament Ravindra Gaikwad.
The party's leader in the house Anandrao Adsul claimed the ban violated the Constitution and the law.
Mahajan, the sources said, urged the civil aviation minister to find a way out to revoke the ban without diluting the charges against the MP.
Gaikwad is said to be staying at a relative's house in Pune now.
"It is not clearly specified anywhere whether airlines can create a no-fly list for all time to come", the same official said, adding, "We will clarify soon".
Gaikwad stayed put at some undisclosed location, saying he had been asked by the Sena leadership to "keep quiet".
"I told him that I have given my complaint to the air-hostess and you refer to him".