After being invited by Leeds West MP Rachel Reeves and city council leader Judith Blake, Chief Secretary to the Treasury Liz Tur said she could not suggest a date "due to diary constraints".
In a letter published by Labour MP Ms Reeves, the Leeds-educated Minister wrote: "I will ask my office to ensure that they reach out when I am next in the area."
The MP said of the letter: "The idea that Treasury Minister Liz Truss is too busy to visit Leeds is an appalling snub to the North and everyone who suffered due to the floods.
“For all its talk of the Northern Powerhouse, this Government does precious little when it comes to taking action or committing funds to help the region."
The row comes as city officials try to get secure funding for Phase 2 of the Leeds Flood Alleviation Scheme, designed to prevent a repeat of the Boxing Day floods of 2015 which damaged more than 700 commercial properties and nearly 3,000 homes.
The Government has made £65m available for the scheme, which is designed to deliver improved defences in Kirkstall as well as locations along the River Aire to its upper catchment.
But a funding gap of £23.3m needs to be bridged before it offers the one-in-200-year level of protection wanted by civic chiefs.
A letter sent in May by Ms Reeves and Coun Blake says: "We would like to invite you up to Leeds to see our plan for the project and meet residents and business affected.
"It is our hope that we can work constructively together to mitigate the flood risk and ensure that homes and businesses are protected for the future."
In her response Ms Truss, who was educated at the comprehensive Roundhay School in Leeds, said the Government "takes flood risk very seriously". She added: "That is why we are investing £2.6bn over six years in our flood capital programme in order to better protect 300,000 homes from flooding by 2021."
Coun Blake said: "We are incredibly disappointed that the Minister has declined to visit Leeds for the foreseeable future. We will continue to put pressure on the Minister, or whoever succeeds her in the role, to honour the commitments made to provide the funding for flood defences Leeds needs and deserves.”