Singh today unveiled the statue of revolutionary Udham Singh at the Jallianwala Bagh here.
"These days, I am seeing that there are incidents of vandalising of statues of great personalities. Indian culture does not permit this even if you do not agree with his (great personality) ideology. But permission to break anyone's statue cannot be given in this country.
"Intolerance and violence cannot be a part of our culture," Singh said while addressing a gathering at the Jallianwala Bagh here.
Clear instructions had been issued to the authorities concerned in this regard throughout the country, he added.
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During his address, the Union minister also talked about the sacrifices made by the likes of Bhagat Singh and Udham Singh in the country's freedom struggle.
Rajnath Singh said the central government had decided to observe the centenary of the Jallianwala Bagh massacre.
Earlier, the Union home minister paid obeisance at the Golden Temple here.
Later, Singh was honoured by SGPC president Gobind Singh Longowal with a set of Sikh religious books, shawls and a replica of Golden Temple.
Longowal also spoke to the minister about the issue of the pending mercy petition of prisoner Balwant Singh Rajona, who was convicted in the assassination of former Punjab chief minister Beant Singh.
The SGPC also demanded an immediate release of Sikh prisoners lodged in the different states for the past several years.
It also sought GST exemption for materials used in preparing 'Langar'.