Mr Brown said he wants its officials to announce at a meeting next week that it will fund the work on making the foreshore of Dalgety Bay, Fife, safe. His call came as plans on how to clear the site were released three years after the waste was discovered.
The Kirkcaldy and Cowdenbeath Labour MP said the publication of four proposals that included concreting over parts of the town's beach on the Firth Of Forth meant the Ministry should now act.
Mr Brown said that having earlier asked its officials "to specifically rule out a do-nothing position that merely left the radiation contamination untreated, we have now made some progress".
He added: "Last year, when the Ministry Of Defence (MoD) was officially named as the polluter, having dumped radiated ash from hundreds of broken-up wartime fighter planes on the Dalgety Bay, it refused to accept the blame.
"I now hope that at Monday's meeting with local people at the Dalgety Bay Forum the Ministry will commit the funds needed to end this unfortunate saga."
Four options were put forward in yesterday's report.
The MoD was told that cutting off access should be considered as part of any attempt to clean up the area. Digging out or concreting some of the beach were the next two options and the fourth, described as the optimised approach, involves elements of the previous three.
Engineering company Amec was asked to look into the options for the area surrounding the Dalgety Bay Sailing Club, next to the former Royal Navy Air Station at Donibristle.
Radioactively contaminated material, radium-226, was found at the site on the eastern coastal margin of Dalgety Bay town.
It is thought to date to instruments from Second World War aircraft dumped at the site.
The 11-acre area covers beach, tidal zone and vegetation. It contains the sailing clubhouse, stores, jetties, slipways and sewer outfall.
The potential risk to people using the area for recreation is considered "significant", the report warns.
It concludes no single technique is best suited to the management of radium contamination, "rather, a combination of techniques is likely to be required to fulfil the management techniques".
It proposed permanent use of "robust" fencing and warning signs, a "clean cover layer" over the site and excavation of source material. The best approach would be a "suitable combination" of the three.
The report was published by the Scottish Environment Protection Agency (Sepa), which has said the MoD is responsible for the contamination.
Its executive director Calum MacDonald said: "This report outlines the extent of management options that could be adopted at the site, ranging from excluding the public from some areas to encapsulating and/or removing the contamination. We will be working towards a solution that is effective and durable."
An MoD spokesman said it was working to establish the extent of funding it could provide to remedy the problem. He added: "We welcome the continuing constructive talks we have had with Sepa and support its efforts to bring all interested parties together to evaluate and take forward the next steps to address the issue."