Mr Kawczynski is leading the setting up of a group of 46 MPs whose constituencies are affected by flooding from the Severn.
He says the issue is the biggest threat to the economic future and prosperity of Shrewsbury, and explained that he told Mr Sunak of the danger of not taking measures to protect towns along the course of the river.
It comes after Shrewsbury, Ironbridge and Bridgnorth suffered severe flooding earlier this year, with many businesses still not recovered from the damage, having been hit by the coronavirus crisis immediately after.
Mr Kawczynski said: "What I said to Rishi Sunak is that the economic damage of not managing the river is mind-blowing."
He added: "We are going to be campaigning very robustly through parliamentary debates, ministerial visits and other measures to ensure that there is finally now, a holistic, long-term strategy and solution to how we manage the river.
"That will mean innovative use of measures like potential wet washland schemes."
Mr Kawczynski added: "Part of the solution will have to be holding back more of the water upstream. There are so many options that can be used either separately or in conjunction with each other."
He said the impact of not addressing the issues would continue to plague residents of the town.
"I see nothing more deleterious to Shrewsbury's economic development than our inability to protect ourselves from flooding. It is the biggest risk to Shrewsbury's long term prosperity and development," he said.
Mr Kawczynski said that by setting up a group of MPs to tackle the issue they were more likely to be able to secure progress.
He said: "In my view the only way we get something done is by going in as a large group."
The MP said that he had seen first hand the impact of this year's flooding on local business and the community, and wanted to make sure it would not be repeated.
"I will never forget going around Coleham and meeting the very many young entrepreneurs, cafe owners, butchers, greengrocers, that were absolutely devastated," he said.
"The people were just absolutely helpless. We have seen flooding in Shrewsbury time and time again and the damage it does so the time has come to work collectively to tackle this problem."