Mr Eastwood was contacted by Will Simpson, a Labour councillor in Denby Dale and also a member of the decision-making cabinet on Kirklees Council.
He was invited to share his views with residents on whether he has confidence in the Prime Minister.
Mr Eastwood replied: “I share your concerns and agree entirely that everybody should abide by the rules, as you did.
“I can confirm I did not attend any parties, nor was I aware of their occurrence.
“I understand your desire to receive a full response. However, the independent inquiry remains ongoing into the incidents, and I firmly believe in due process.
“It is important that this inquiry should be allowed to be concluded, but please be assured I shall respond fully to you in due course.”
Coun Simpson, who lives within Mr Eastwood’s constituency in Clayton West, described the response as “generic” and “as pathetic as it is predictable”.
He said: “[It] should be pretty basic for an elected MP to be able to say that they have confidence in their own PM if they do and respect their residents enough to be honest with them."
The Local Democracy Reporting Service wrote to Mr Eastwood and asked: “Does the Prime Minister have your support or should he resign?”
Mr Eastwood reiterated his stance, commenting: “I am waiting for the publication of the independent Sue Gray report, to establish the facts before making any further comment.”
Mr Eastwood was elected in the Conservative landslide at the 2019 General Election, winning against Labour’s Paula Sheriff.