Mulayam's cousin and SP's national general secretary Ram Gopal Yadav, who is seen as backing the Chief Minister, said the leadership had committed an unintentional "mistake" by removing Akhilesh as party's UP president.
He blamed "outsiders" for the crisis, an apparent reference to Amar Singh who recently returned to the party after a number of years.
In the evening, Mulayam rushed here from Delhi and launched efforts to douse the flames by meeting Akhilesh as well as Shivpal.
Shivpal later met Akhilesh at his official residence, sources said, adding the meeting came at the behest of Mulayam.
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Immediately thereafter, the SP chief met Akhilesh, the sources said.
"Once he (Mulayam) reaches here, all will be well. His word is final," Ram Gopal said earlier.
Earlier in the day, Ramgopal had met the Chief Minister and claimed that "Akhilesh is not angry with anyone and the decision of netaji (Mulayam) is final in the party."
The same was said by Shivpal at his press conference.
The feud had spilled into the open after the Chief Minister stripped Shivpal of key ministerial portfolios on September 13, hours after he was replaced with Shivpal as the party's state unit chief by his father.
"Differences do take place on some minor point and they can be resolved.... The leadership, though not deliberately, had made a mistake when CM was removed from the post of (state) president (of SP)," Ram Gopal told reporters.