Lautenberg - speaking the day before his 89th birthday - also vowed to take on the gun lobby, cracked jokes, and said he had unfinished work to do, but did not answer one of the biggest questions in New Jersey politics: whether he will seek another six-year term in 2014.
"I've got a lot of work to do yet, serious things, and we pride ourselves with my office and my team on getting things done. That's the focus. I'm not thinking about the politics right now," Lautenberg said in his first public comments in weeks. Asked if there was a chance he would not run again he said, "I don't see that, but who knows?"
Booker's campaign declined to comment Tuesday. On Twitter, however, Booker wrote: "Often your best words are those you choose to keep to yourself."
Lautenberg, who has been in the Senate for most of the last 20 years, displayed a sense of ownership.
"It's an open seat if I don't keep it," Lautenberg said. When a reporter asked if he would run against Booker, the senator said the question was backward. "Run against him? Would he run against me?"
He later said Booker was "entitled to do it" if he wanted to challenge Lautenberg.
"He'll have to stand on his record, and I'm sure he won't be a lone soldier out there drooling at the mouth and wanting this cushy job," Lautenberg said.
With most Democrats passing on the chance to run against Gov. Christie this year, many are eyeing Lautenberg's seat in 2014 - though, unlike Booker, the rest of the possible field has avoided talking about it publicly.
Booker, by contrast, used a Web video to announce that he was considering a run, and recently filed papers to create a Senate campaign committee. Early polls rate him as the Democratic favorite in 2014.
Booker, at the New Jersey State Society inaugural ball in Washington on Sunday night, evaded questions about whether he would run.
The senator said Tuesday that he and Booker shared a commitment "to working in Newark. ... I go there every day, I can tell you that."
Lautenberg had been almost entirely out of public view since mid-December, missing several critical votes, including those on the fiscal cliff deal and a relief package to aid the victims of Hurricane Sandy.
He said he had a cold that became the flu, followed by "a severe case of bronchitis, with fluid in the chest." He said he was well now.
On Tuesday he reintroduced a bill to ban high-capacity gun magazines, a long-held goal that has new momentum with backing from President Obama after the Newtown school shooting.
As for the cane, Lautenberg said, "I don't need this, but it adds cachet."
Contact Jonathan Tamari at firstname.lastname@example.org or follow him on Twitter @JonathanTamari. Read his blog 'Capitol Inq' at www.philly.com/CapitolInq.