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Captain Singh's assent came after a meeting with Congress's Punjab in-charge Harish Rawat who flew in a helicopter from Delhi to meet the Chief Minister in Chandigarh. Sources said Captain Singh agreed to accept any decision taken by party chief Sonia Gandhi.
However, Captain Singh also said that he should be involved by the party leadership while taking important decisions and that Mr Sidhu's appointment should complement his efforts in helping the party come back to power in the next year's elections, sources said.
The 79-year-old also demanded that he be given a free hand in reshuffling his cabinet and in the appointment of working presidents under Mr Sidhu.
But in signs that not every difference had been swept under the rug, Amarinder Singh is also learnt to have told Mr Rawat that he will not meet Mr Sidhu till he publicly expresses regret or apologises for his tweets against him.
According to sources, the compromise formula involves Mr Sidhu's elevation as Punjab Congress President and the appointment of three working presidents who will be picked by Captain Singh. The Chief Minister's cabinet will be expanded too and Hindus and Dalits and will be given priority.
The breakthrough came as Navjot Singh Sidhu held a series of meetings with senior party leaders in the state including the Punjab Congress Chief and tweeted that he was "seeking guidance", dropping a big hint even as the announcement of his takeover was held up.
"Seeking guidance of Presidents of the illustrious Punjab Pradesh Congress Committee ... Conversations with wise men, worth months of Education !!" Mr Sidhu tweeted with along with pictures.
The meetings came a day after sources said Captain Singh had written to Sonia Gandhi objecting to Mr Sidhu replacing Sunil Jakhar as the party's state chief - a solution reportedly arrived at by the party following a series of separate meetings between the Gandhis, Mr Sidhu, and Mr Singh.
Separately, Navjot Sidhu met with Sonia Gandhi and Rahul Gandhi on Friday in Delhi after the feud saw a dramatic escalation a day before when both Amarinder Singh and Mr Sidhu rounded up MLAs and ministers on their side and were deep into separate meetings.
The rift between Amarinder Singh and Navjot Sidhu, festering since the Congress won the Punjab election in 2017, has endangered the party's re-election bid next year. Mr Sidhu, who quit the BJP and joined the Congress just before the 2017 election, has been fighting for a bigger slice of power but so far, Mr Singh had been resistant to the idea.