A no confidence motion against Wigneswaran was handed over to Governor Reginald Cooray with the signatures of northern provincial council members on June 15.
Some 22 out of the 38 provincial council members had signed the motion after Wigneswaran's move to sack some ministers of his administration, triggering crisis in the northern council.
"He will not be removed. All four parties within the TNA are firmly backing the chief minister," M K Shivajilingam, a member of the northern provincial council and Wigneswaran's supporter said.
A committee appointed by the chief minister last year submitted its report last week. It found evidence on the charges made against the two ministers.
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Wigneswaran, a former top judge, had asked the two ministers in the four-member cabinet to resign so that allegations against them can be investigated.
He has been at loggerheads with TNA's moderate faction since early 2015.
The TNA's moderate faction has been backing the government's reconciliation programme. However, Wigneswaran has expressed dissatisfaction with the government's delivery of reconciliation pledges.
This was following a counter resolution in support of the chief minister signed by 15 members.
However, Vannihamige Jayathilaka, one of the two Sinhala members in the council said Wigneswaran must be removed as over the last three years he had done nothing.
"He is not a northerner, sent from Colombo. He is connected to Sinhalese through family marriage," Jayathilaka said.
The TNA sources said despite sharp differences with Wigneswaran, the issue may be amicably settled without him being removed.
Wigneswaran, who became first ever Tamil elected chief minister in 2013, met religious leaders in the north yesterday to shore up support for himself.
Most shops were closed and public transport was at a standstill in support of the strike.