"Our family is grappling with a colossal tragedy. This is not the time to create any controversy on a memorial for the Shiv Sena chief," Uddhav said in a statement.
"I appeal to you with folded hands - kindly help us to remain calm in this tragic time. Those attempting to rake up any controversy should understand our predicament," he said.
He said the sea of humanity of 2.5 million which turned up to pay its last respects to the Sena chief was calm and disciplined.
"I salute their spirit and grit in the tragedy. Even the decision on a memorial will be taken by these Shiv Sainiks. I shall not come in between the Shiv Sena chief and the Shiv Sainiks," Uddhav said.
Uddhav's statement came in the wake of a controversy following a demand by Sena leader Manohar Joshi for a memorial to Bal Thackeray at Shivaji Park, where he was publicly cremated Sunday.
While the Maharashtra government appeared favourably inclined to the move, several groups and some activists have opposed the proposal.
Even as the debate rages in Mumbai, in adjacent Thane, the civic body is planning to erect a huge statue of the departed leader outside its headquarters.