The press office at the Housing and Urban Development Department is keeping careful track of what it sees as negative stories about Secretary Samuel R. Pierce Jr.

The media watch began last spring, when The Wall Street Journal published a rather unflattering profile of Pierce. The story, by reporter Timothy D. Schellhardt, said the secretary appeared reclusive and uninterested in his job and seemed to have little clout within the Reagan administration.

It said Pierce may have been disturbed by a new nickname for him that had been making the rounds: "The dud at HUD."

This prompted Leonard Burchman, Pierce's assistant for public affairs, to rebut the Journal article in a 12-page memo to key HUD officials. The title: "Anatomy of a Hatchet Job."

Burchman trotted out his best statistics, saying that Pierce has spoken to 145 groups, or an average of 1.4 speeches per week. "It is hard to see how the reporter could honestly characterize the secretary as reclusive," he wrote.

The memo brushed aside suggestions that Pierce is uncomfortable running HUD or ill-prepared for the job. "Untrue on both counts! The secretary feels extremely comfortable in his position."

Burchman also objected to a description of Pierce's trip to China last summer, saying: "Surely the effect is to make the Far East trip appear trivial, and the secretary look vacuous."

As for Pierce's nickname, Burchman wrote: "Such a characterization can hardly 'disturb' the secretary, since he has never heard it . . . . So far as he knows, it came from the fertile imagination of the Journal writer."

He concluded that the article "was so filled with inaccuracies, distortions and outright untruths that it can best be referred to as a 'hatchet job.' "

The Wall Street Journal said in a letter to HUD that it stands by the story. But the newspaper began to receive letters defending Pierce, after various interest groups reportedly were asked to speak up for the secretary.

"I have no problem with . . . telling anyone that I have complained about cheap shots," Burchman said this week. "I wanted our staff people to get the other side of the coin. It's helpful for them to fully understand the man as I see him. The man is not a recluse. He does get out and talk to people."

Burchman also criticized an article on Pierce in last week's National Journal. Among other things, he challenged the assertion that Federal Housing Commissioner Philip Abrams (a leading candidate for the job of undersecretary) has little access to Pierce, and he asked Abrams to write the magazine to rebut the story on that point.

In a further effort to beef up HUD's press operation, the White House has nominated Robin Raborn to the new job of assistant secretary for public affairs. Raborn is a respected professional who helped publicize administration attacks on fraud and abuse while at the Office of Management and Budget.

At Raborn's Senate confirmation hearing, however, Sen. William Proxmire (D-Wis.) said it seemed "illogical" to create a new assistant secretary's post at a time when HUD was laying off staff. He said the timing suggests that "this is to advance the political fortunes of the Republican Party in 1984."

But Raborn said her main job is to improve management of the 41-person press office. She said she already has saved $47,000 a year by eliminating one of two editions of HUD's daily news summary and distributing it to more people with fewer staff.

"They happened to pick the tightwad of the year when it comes to public affairs," Raborn said. "I'm not going to put in a lot of fluffy PR. There will be no publications with pictures of political appointees." * * *

DOG DAYS . . . John A. Maxim Jr. is barking up the wrong tree with his expense account, the General Accounting Office has ruled.

Maxim, an assistant general counsel at HUD, was sent to Seattle for six days in February. He submitted a $105 bill for the cost of boarding his dog at K-Kennels International in Chantilly, Va., saying there was no one to take care of the pet while he was away. The GAO tersely rejected the claim, saying: "Absent statutory or regulatory authorization, kennel costs may not be reimbursed."