Defence Secretary Ben Wallace meeting Ukrainian soldiers being trained at a British Army base in Dorset
Contrasting their responsibilities, he said Mr Mercer was a "junior minister" who "doesn't have to run the budget".
Mr Mercer has claimed it is "not credible" for Mr Wallace to say the UK military has been "hollowed out".
His wife, Felicity Cornelius-Mercer, accused the defence secretary of treating her husband with "disdain".
Both men are former army officers. Mr Wallace is a full cabinet member, while Mr Mercer is a lower-ranking minister, with a lower salary, who attends cabinet meetings when needed.
The veterans' affairs job is a position within the Cabinet Office, having previously been part of the Ministry of Defence.
During a debate in the Commons last month, Mr Wallace said: "We have been hollowed out and underfunded".
Days later, in what was widely seen as being a message directed at the chancellor ahead of the Budget, he told a news conference in Portsmouth a "growing proportion" of government spending would need to be devoted to keeping the country safe.
The defence secretary's comments came against a backdrop of UK efforts to help Ukraine repel invading Russian troops and rising global tensions with China.
But on Wednesday, Mr Mercer told LBC radio: "Ben is engaged in a lobbying effort for his department, as you would expect him to be.
"The facts are that when I came into politics [he became an MP in 2015], defence spending was around £38bn per year - it is just shy of £50bn a year now.
"It is obviously not credible to say that the money has been taken out of defence."
Responding on LBC on Thursday, Mr Wallace said: "Johnny is a junior minister, and Johnny luckily doesn't have to run the budget.
"I have a defence budget that has to deal, like all the other budgets, with inflation, with changes to threat, and I have to just deal with that. And that's my job."
Asked if Mr Mercer was being naive, Mr Wallace said: "No, no, no. I just think, you know, his experience is not... he's not the secretary of state.
"I run a department of 224,000 people", while "he's got 12 people in the office."
This prompted Felicity Cornelius-Mercer to spring to her husband's defence, tweeting: "Wow. The disdain from @BWallaceMP for @JohnnyMercerUK and his office for veterans affairs really is something else.
"You may start to realise why care for veterans is such a daily battle."
Downing Street said both the Ministry of Defence and the Office for Veterans' Affairs did "vitally important work to support the UK".
Asked which of the two ministers best expressed the government's view on defence spending. the prime minister's spokesman said: "I think the defence secretary has made it clear on a number of occasions that defence spending turned a corner under this government due to the spending review in 2020.
"It provided an uplift of £24 billion over four years, and of course additional funding has also been provided for Ukraine."
Future defence spending was a "live issue" ahead of next month's Budget, the spokesman added.