Representative Thomas Kean Jr. is back at work — and back to avoiding the spotlight.

On Monday, Mr. Kean, a New Jersey Republican, silently refused to even acknowledge a reporter as he hustled out of the Capitol toward Independence Avenue. He did much the same on Thursday, when he was one of the last lawmakers to descend the Capitol steps after the House recessed for the week.

Asked about his return to Congress after a monthslong absence and his schedule as he runs for re-election in one of the country’s most competitive contests, Mr. Kean stared straight ahead.

If the congressman has been on the campaign trail in New Jersey, it is hard to tell. Aides have refused repeated requests for his campaign schedule in the two weeks since Mr. Kean reappeared in Congress and explained that he had been hospitalized for depression.

He did not follow up a June 30 speech on the House floor with media interviews. And even some of his staunchest allies in New Jersey said they were unaware of his plans to campaign locally.

The Republican chairman in Sussex County, a region seen as crucial to Mr. Kean’s victory, says he is “waiting on dates” for a hoped-for visit from the congressman. State Senator Doug Steinhardt, the chairman of the Republican Party in Warren, a neighboring county and conservative part of Mr. Kean’s district, said the congressman was expected to attend the county fair at the end of July. But he was aware of no other scheduled campaign events.

“I hope he intends to be more visible,” said Mr. Steinhardt, who previously led the New Jersey Republican Party.

Harrison Neely, a spokesman for Mr. Kean, said that the congressman was “full speed ahead with a campaign.”

“You can see that the congressman is active,” Mr. Neely said. “His social media is active.”

Since his June 30 return to Congress, Mr. Kean’s social media accounts have shared only a handful of posts that include recent photos of the congressman. One shows him marching with his wife in a parade. Another features him in an office, beside a family concerned about Lyme disease, an increasing worry in the area. There are also images of him with winners of an elementary school essay-writing contest and speaking at recent House committee hearings.

In some ways, Mr. Kean, 57, is operating as he always has. He has refused to hold in-person town hall meetings during his two terms. And he has shunned most media attention during his tenure. Mr. Neely noted that it was not unusual for Mr. Kean to decline to share his schedule of upcoming public appearances, as he had not done so during his previous congressional campaigns, either.

But Mr. Kean’s recent mental-health struggle and long absence — which he declined to explain in any detail for nearly four months — have increased his profile and brought a higher level of scrutiny to his campaign as he makes his pitch to voters. He is facing a tough race for a third term against Rebecca Bennett, the Democratic nominee, in a swing district that both parties consider a must-win in the midterm battle for control of Congress. His fate in November may depend in part on how he manages to shape the narrative of his return.

It may also hinge on how shrewdly he can navigate new headwinds. President Trump’s low approval ratings and voter dissatisfaction over the prices of gas and food have made Republicans like him vulnerable. In New Jersey, Mr. Kean, who was endorsed by the president, has had to fend off claims that he failed to stand up to Mr. Trump when the president tried to cancel funding for a Hudson River train tunnel vital to commuters in the district.

He has also had to weather the administration’s abrupt changes in policy tied to a proposed migrant detention facility in Roxbury, N.J., a Republican stronghold in Mr. Kean’s district. The Trump administration last month said it had abandoned its expensive quest to build the detention center in a vacant warehouse, but last week signaled plans to revive the project. Republican leaders in the township, who have sued to block the 1,500-bed jail and months ago criticized Mr. Kean for failing to do enough to try to stop it, again began raising the alarm.

The mayor of Roxbury, Shawn Potillo, also contacted Mr. Kean’s office.

“As he resumes his official duties, we welcome any support he may be able to provide,” Mr. Potillo said in an email.

Mr. Kean’s most recent campaign finance filings point to the ground he lost while out of the public eye from March through June.

A report his campaign filed Wednesday with the Federal Election Commission showed receipts of roughly $500,000 in the last quarter, far short of the $1.6 million Ms. Bennett reported.

Mr. Kean nonetheless continues to hold a sizable fund-raising edge, with $3.6 million left on hand to spend in the run-up to the Nov. 3 election for his Seventh District seat. Ms. Bennett, a former U.S. Navy helicopter pilot who has worked for health care companies, has less than half as much: $1.4 million.

The congressman also has the advantage of name recognition in a district where registered Republicans outnumber Democrats by roughly 19,000 voters. His father, who is also named Thomas Kean, was one of the state’s most popular governors and later steered the 9/11 Commission.

And he does still have time. Jeanette Hoffman, a Republican political strategist, noted that summertime is a typically slow season for campaigning. She said she was confident that Mr. Kean would run a “vigorous campaign when it matters most.”

“I don’t think anybody’s looking at his calendar and saying, ‘Oh my gosh where is he?’” Ms. Hoffman said. “That’s an insider’s game right now.”