They conveyed their demand to AICC general secretary and state in-charge Gurudas Kamat in a meeting at Vaghela's bungalow in Gandhinagar last night.
State Congress president Bharatsinh Solanki was not present at the meet, but he later said the party has several competent leaders, including Vaghela, and one of them can be projected for the top position.
Of the total 57 Congress MLAs in Gujarat, 36 attended the meeting and endorsed the 76-year-old politician's name as the CM's face, said Gyasuddin Shaikh, a party legislator from the city.
"During the meeting, all these 36 MLAs demanded that our Leader of Opposition Shankersinh Vaghela be declared as the CM candidate. This will increase our chances of winning the polls," said Shaikh.
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"I openly told Kamatji that the Congress has to project Vaghela as the CM face if the party is to win more than 60 seats (in the 182-member House).
"Vaghela is a true mass leader. Some MLAs even told Kamatji that they would not contest the polls if Vaghela is not declared the candidate for the top post," said Shaikh.
Another Congress MLA Ramsinh Parmar said the party's central leadership should decide on Vaghela's candidature at the earliest.
"The Congress is out of power for the last 20 years. Thus, many of us clearly said Vaghela must be given a free hand in these polls if the party wants to form the next government. We urge the party high command to make an announcement in this regard at the earliest," Parmar told reporters after the meet.
"Since the meeting was called at a short notice, many MLAs could not come. Otherwise, all were invited," said the MLA from Rajkot.
Meanwhile, Kamat claimed the discussion at the meeting largely revolved around the party's preparedness for the polls, expected in the second half of 2017.
"We discussed our preparedness for the elections. Many MLAs wanted to know their status (chances of getting the ticket). Many even complained they are being lured by the ruling BJP," Kamat told reporters.
Vaghela, however, declined to comment on the stand taken by his supporters at the gathering but added he is ready to make way for a Patel community MLA to take over as the Leader of Opposition.
He also sought to play down the absence of Solanki.
"Solanki came back from the US last evening. If he would have arrived early, he may have been called too. Our meeting was not convened secretly. It was all about charting out a strategy against BJP," said Vaghela.
Solanki today held a press conference, where he said the MLAs have all the right to express their feelings to the party high command.
Asked if he agreed with the demand made by the MLAs at the meeting, he said the Congress has several capable leaders, including Vaghela, and the party can win the elections if one of them is projected for the top post.
"We have many prominent leaders such as Vaghela, Arjun Modhwadia, Shaktisinh Gohil, Kunvarji Bavalia, Siddharth Patel and Jagdish Thakor. The Congress can win with a two-thirds majority if any one of them is projected as the CM candidate," said Solanki.