Mr Reid has spoken of "anonymous forces, always in the dark", trying to divide the two men, who have been trying to establish who does what under devolution. He accused "someone with an axe to grind or someone who wants to climb the ladder" of poisoning the political atmosphere.
His remarks echoed those of his cabinet colleague Clare Short, who once attacked Labour's spin-doctors as people "who live in the dark".
The clash reflects confusion about the role of the Secretary of State for Scotland now that many powers have been devolved from Westminster to the new Scottish Parliament.
Last week, for example, Mr Dewar's camp was angered at the credit claimed by Mr Reid for saving the Kvaerner shipyard in Govan, Glasgow. Mr Reid had been involved in talks to persuade Kvaerner to sell to GEC Marconi. A press release from Mr Dewar's officials praising Mr Reid's role was replaced by another containing no mention of Mr Reid.
In another incident, Mr Dewar called a press conference in Edinburgh to announce the Scottish areas proposed for regional assistance from the European Union. This subject is still reserved to Westminster, so Mr Reid found himself holding a similar press conference in London at the same time.
Mr Reid's role, as Scotland's man in the Cabinet but without much spending power, is to secure the Union after devolution. Mr Dewar, meanwhile, has an interest in playing down his colleague's role because he faces nationalist criticism that a devolved Scotland is really still being run from Westminster.
Earlier this week, Mr Reid delighted colleagues by resisting William Hague's suggestion that Scottish Westminster MPs should be barred from voting on English legislation.
Tam Dalyell, the Labour MP for Linlithgow, has said: "John Reid is a very thrusting politician and now turf wars have broken out with Donald - I don't know what else people expected."Reuse content