He also said that the party's demand to have the returning officer of the constituency removed was being looked into, while deploring "attempts to cast aspersions on the ECI at a very sensitive juncture of the poll process"a, which also "cause long-term damage" to the institution.
On the permission sought by BJP to hold a rally in Beniabagh, Sampath said that the poll panel took the feedback from the Varanasi district magistrate, who is also the returning officer and it was "decided that permission could not be granted on security grounds".
"When issues of security and suitability are involved, the commission would go by the professional advice and expertise" of the local authorities, he said.
Sampath said that an appeal was made by the Bharatiya Janata Party Wednesday to review its request to hold the rally at the venue.
"After consulting the chief secretary and the director general of police of the state (Uttar Pradesh), no reason was found to deviate from the decision taken on the advice of the local authorities," he said.
"This has unfortunately become a bone of contention where security and suitability issues were involved. The EC would naturally go by professional advice and the local administration cannot be ignored," he added.
"I do not think the Election Commission can be faulted...We have always acted in the interest of upholding the constitution," he added.
The CEC asked the political parties to "understand" when permission to hold rallies could not be granted due to certain "complexities" involved.
"We deplore attempts to cast aspersions on the EC at a very sensitive juncture of the poll process. This could cause long-term damage to the EC," he said.
On the issue of removing the Varanasi returning officer, as demanded by the BJP, Sampath said that in denying permission to hold the rally at Beniabagh, the officer had tendered his "professional advice".
However, he added that the BJP has presented "more instances" of alleged lack of neutral conduct on the part of the RO and that they "will be inquired into".
"Officers are transferred only when necessary, after we have made our independent verification," he said.
Thousands of BJP activists protested in Varanasi and New Delhi against the Election Commission's curb on the Beniabagh rally.
Before Modi flew into the Hindu holy city Thursday evening to address one rally that got the poll panel's green signal late Wednesday, a virtual army of BJP workers and leaders staged noisy demonstrations outside the Banaras Hindu University and the district magistrate's office.
Sampath also said that the EC was looking into the complaint that Congress vice president Rahul Gandhi was present at a booth inspecting an electronic voting machine in Amethi while polling was on Wednesday. "We have asked for a factual report on the matter," he said.