Will Alexander, who played Dr Marc Peders in Shortland Street, made the plea at a public forum during the council's meeting on Wednesday.
Alexander has just ended a 19-day hunger strike protesting about the war, which began in October last year.
He called on the council to also write to Prime Minister Christopher Luxon and Foreign Affairs Minister Winston Peters to increase funding to UNRWA (United Nations Relief and Works Agency for Palestine Refugees), investigate Auckland-based tech company Rakon and to approve humanitarian visas for Gazans.
New Zealand had suspended aid to UNRWA because of allegations against 12 of its employees; these allegations had been proven to be "baseless", he told RNZ's Checkpoint programme last month.
A UN report to this effect had so far not made the government change its decision, he said.
Alexander also told Checkpoint he would not start eating again until the government stopped participating in the bombing in Yemen and withdrew New Zealand troops from the Red Sea.
He also tried to enlist the support of MPs early on in the hunger strike with some expressing concern for him.
