SAN JOSE — For weeks, San Jose police Officer Phillip White had been using his personal Twitter account to vent displeasure over the ongoing protests in Oakland and around the country about the deaths of unarmed black men at the hands of law enforcement.

But when his posts turned threatening last weekend, White learned just how far-reaching words can be on social media. The San Jose Police Department placed White on administrative leave Monday as the furor over the officer’s posts showed no signs of abating.

An online petition at change.org demanding his firing gained over 5,000 signatures in less than a day. Civic leaders questioned how he can continue to be an effective cop. Menlo College, where White was an assistant basketball coach, cut ties with him.

The most inflammatory tweets, which evoked the strongest social-media reaction, read, “Threaten me or my family and I will use my God given and law appointed right and duty to kill you. #CopsLivesMatter” and “By the way if anyone feels they can’t breathe or their lives matter I’ll be at the movies tonight, off duty, carrying my gun.”

Community leaders, particularly advocates for minority groups, called on the police department to fire White.

“I couldn’t believe it was real, that he would put his face out there in the Twittersphere and make these statements as if he’s baiting the public to engage in a violent altercation,” said Walter Wilson, who sits on the board of the city’s African American Community Service Agency. “If this is real, he should not have a gun and a badge. The police department deserves better than this guy.”

San Jose police Chief Larry Esquivel said in a statement that White’s posts do not reflect “the thoughts or feelings” of those on the force.

“The San Jose Police Department recognizes the sensitive nature of this matter,” added Esquivel’s statement, which announced White is on paid leave while an investigation is conducted.

Independent Police Auditor LaDoris Cordell said her office forwarded a community complaint about the tweets to the department’s internal-affairs unit, where White was once assigned. The department also received a direct complaint.

The police union spoke out against the posts without mentioning White by name.

“Offensive, disrespectful and inappropriate social media comments have no place in the public discourse surrounding the tragic loss of life from recent officer involved incidents,” according to a statement. “We condemn these comments.”

White also lost his coaching position at Menlo College, which said in a statement that the school “will not be represented by expressions of intolerance and bigotry on the campus, on social media, or on the Internet.”

Mayor-elect Sam Liccardo said he hopes the posts don’t taint the broader department.

“It undermines everything that our officers are working to accomplish in our police department to build relationships with trust in our community, and I’d support the chief taking any and all disciplinary actions, including termination, to ensure this kind of conduct does not continue,” he said.

White, a 20-year-veteran officer, could not be reached for comment Monday. An October story in this newspaper detailed his success with a pilot gang prevention education program for schoolchildren.

The controversy marks the latest black eye the department has received nationally. This fall, the department was roundly criticized when a sergeant moonlighting for the San Francisco 49ers complicated a domestic-violence investigation involving defensive lineman Ray McDonald, who ultimately was not charged.

San Jose police officials have said they have a policy not to post in ways that would constitute “conduct unbecoming of an officer.”

White’s Twitter posts, which were first reported by Buzzfeed on Sunday, are protected speech under the First Amendment, said Steven Clark, a legal analyst, defense attorney and former prosecutor. But they do not preclude him from discipline if they prove to diminish his effectiveness as a police officer.

“Because of the nature of his job and his interaction with the community, it creates a problem,” Clark said. “At a time when police should be building bridges with communities, this is the opposite of that.”

Lauri Stevens, a Boston-based social media strategist who works with law enforcement, agrees the First Amendment gives officers the right to state their opinions, but that doesn’t mean it is wise. She urges police to actively tell their story — like all the good things they do.

“But they have to keep it positive,” Stevens said. “And if they’re thinking about saying something that they probably shouldn’t, then they should just not say it.”

Cops, she added, are feeling like their profession is under siege. This officer, she said, might have been expressing what is a common frustration — that their lives matter, too.

“He’s angry just like the protesters are angry,” Stevens said. “They can say what they want. But because he’s a police officer, he can’t.”

Demonstrators have been protesting what they view as rampant racial injustice by law enforcement.

They have occurred in the wake of grand juries declining to indict white officers in the deaths of African-Americans Michael Brown in Ferguson, Missouri, and Eric Garner in Staten Island, New York. Garner’s last words — “I can’t breathe” — have become a rallying cry, and #BlackLivesMatter now is a common social media hashtag.

Staff writer Mike Rosenberg contributed to this report.