Raut resigned after his election to the Lok Sabha from Ratnagiri-Sindhudurg parliamentary constituency.
Today was the last date of withdrawal of papers.
Congress candidate Mohan Joshi said he had received instructions to withdraw from the fray.
"I will obey the party orders. This decision was taken at the meeting between Chief Minister Prithviraj Chavan and NCP president Sharad Pawar last night," he said.
Chavan had yesterday said that talks with NCP were not conclusive before Congress decided to put up its candidate on the last day of filing of nomination.
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Meanwhile, when contacted, state Congress President Manikrao Thakare said all senior leaders were of the view that the party should contest the by-election. "It was our seat and we had 24 votes more than the NCP," he said.
Thakre said he had also mentioned yesterday that the final decision would be taken by Chavan and Pawar.
"Accordingly, our candidate has been asked to withdraw," he said.
To a question on whether the Congress had given in to NCP pressure, Thakare said, "there is no question of pressure. In coalition, there has to be adjustments. Afterall, NCP had fielded their state unit chief."
With Tatkare's election, the strength of NCP in the 78-member Legislative Council goes up to 29. Congress has 22, BJP 11, Shiv Sena six, Lok Bharti, PWP and PRP one each, Independents seven.
The Legislative Assembly was the electoral college for the by-election.