The President was to attend a function in Mumbai and then proceed to Shirdi on Friday for some functions associated with the Shri Saibaba Sansthan Trust.
Meanwhile, security was stepped up in Mumbai on Thursday to prevent any unrest as Bal Thackeray was reported in a "very critical" condition in hospital.
Large crowds of supporters gathered overnight outside the residence of ailing 86-year-old Thackeray, who founded the right-wing Hindu party Shiv Sena.
"We have a lot of forces on the roads. Extra measures are being taken," Mumbai police spokesman Nisar Tamboli said.
In the early hours of Thursday, Thackeray's son Uddhav emerged from the house in the suburb of Bandra to reassure the crowds and ask them to pray for his father.
"We are hopeful. You be hopeful. Let's pray," he said.
"Bal... has strong will power. We'll come out from the problem. Don't trust rumours. Make peace," he was quoted as saying by PTI agency.