Batts is in "continuing conversations with the mayor and city staff concerning his future" in Oakland, according to a statement issued by the Oakland Police Department.
"I have not made a final decision as to my future with this agency. It still needs to be determined if I am a fit for the city of Oakland's vision of the future," Batts said in a statement.
"The demands on the Oakland Police Department are great, youth violence is of great concern, and we have experienced a recent spike in violent crime. In order to make significant improvements to the quality of life for the residents, collective coordination and cooperation must be a priority for ensuring public safety."
In a reference to the city's decision to lay off 80 officers last year because of its budget deficit, Batts added, "I continue to have concerns surrounding the support and resources being provided and am committed to doing whatever is required to fix the broken systems within this agency."
Batts was one of two finalists for the San Jose job, along with Chris Moore, who has been that city's acting chief since Rob Davis retired in October.
Batts applied for the San Jose job in October but didn't tell Oakland officials about it until several weeks ago.
Today's statement didn't specify if Batts decided not to pursue the San Jose job anymore or if San Jose officials chose Moore over him. San Jose officials were unavailable for comment.
The statement said Batts "wishes his good friend and colleague, newly appointed Police Chief Chris Moore, the best of luck."
Oakland officials said they hoped Batts would stay in Oakland long-term.
"I am optimistic that the chief will continue to serve the city," Mayor Jean Quan said in a statement. "Since I became mayor, Chief Batts and I have talked on a nearly daily basis to work together to protect officer and citizen safety in Oakland.
"I appreciate his leadership and commitment to community policing and to raising professional standards."
City Council President Larry Reid agreed.
"A lot of people want him to stay, and I'm first in line," Reid said.
He said he has received more than 100 phone calls from constituents encouraging him to do everything he can do to convince Batts to stay.
However, Reid said Batts "needs to have a press conference to let the community know that he would like to remain as chief of police."
Oakland police union president Dominic Arotzarena concurred, saying it's important for Batts to "let the officers know that he's devoted to staying here."
Arotzarena said he hopes Batts stays in Oakland so "we don't have to go through the process of looking for a new chief."
He said officers wouldn't resent Batts for applying for the San Jose job.
"We're big boys, and we won't hold it against him," Arotzarena said.
Other officials also said it needs to be clear that Batts is committed to Oakland.
City Councilwoman Jane Brunner said Batts "is a terrific chief, but he has to want to be in this city."
Brunner said she and other City Council members didn't know until recently that Batts was applying for the San Jose job and was unhappy in Oakland.
She said Batts needs to "start a dialogue" with city leaders about what must be done to make him happy in Oakland.
City Councilman Ignacio De La Fuente said he supports Batts, but that his decision to apply for the San Jose job "caused disruption and unrest" among police officers and the city at large.
De La Fuente said the Police Department is "going through a very difficult time" because of the city's financial problems, and that the situation will get even more difficult because preliminary estimates are that the city will face a $46 million deficit in the next fiscal year.