Kepong MP Lim Lip Eng said S Vigneswaran should either relinquish his position as Dewan Negara president or resign from his newly-elected position of MIC president.
"It is the convention for political appointees to step down from their positions once a new government was installed after a general election.
"This is to make way for the Pakatan Harapan federal government to appoint a candidate of its choice.
"If he insists on holding on to the president's chair, then he should, as shown correctly by our new Dewan Rakyat speaker, resign from his position in MIC," said the DAP lawmaker.
Former Court of Appeal Judge Mohamad Ariff Md Yusof had resigned from his positions in Amanah following his appointment as Dewan Rakyat speaker.
Lim, who is a lawyer, said Mohamad Ariff is known in the legal circles as an independent-minded person with a great sense of impartiality, fairness and no-nonsense.
"However, over at Dewan Negara, we see the opposite. We have the Dewan Negara president being elected as the MIC president recently.
"The MIC president can thump his chest and proclaim his impartiality, but we all know where his alignment and loyalty lies," he said.
Vigneswaran was appointed as the Dewan Negara president on April 26, 2016, under the then BN government.
He was elected uncontested as the new MIC president last week.