San Francisco Mayor London Breed said Monday that she’s ready to confront the controversies and neighborhood squabbles that will inevitably accompany her attempts to grapple with the city’s homelessness crisis and housing shortage.

Speaking at an event hosted by the Public Policy Institute of California, Breed told PPIC President and CEO Mark Baldassare that though she’s sensitive to calls by some to “maintain neighborhood character,” the humanitarian imperatives of the city’s two biggest problems had to come first if San Franciscans want to see progress.

“The need to build more housing is critical to our ability to provide places for people to live,” Breed said. She has committed to adding at least 1,000 shelter beds for homeless people by 2020 and getting 5,000 units of housing built annually.

Since taking office in July, much of Breed’s work has centered on chipping away at bureaucracy holding up new shelter and housing development.

“Everyone wants to do that, but as soon as we want to build it in some neighborhoods, we’re met with a lot of opposition,” Breed said. “Every neighborhood has to share in an increase of housing units. It’s the only way we’re going to get to a better place.”

It wasn’t unreasonable, she added “to expect to build a little bit taller — four, five, sometimes six stories — where it typically may not be zoned for that particular purpose.”

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Her remarks follow a pair of contentious meetings last week on her proposal to build a 200-bed Navigation Center — a 24-hour shelter with intensive services meant to guide people to stable housing — on what’s now a parking lot on the Embarcadero.

The concept was met with resistance from people who said they live near the proposed site. Many were concerned the homeless people residing at the center would bring dirty, dangerous behavior to the tourist-heavy neighborhood and urged city officials to find other locations for it, considering the volume of homelessness services already in supervisorial District Six, where the site lies.

“It’s a very controversial thing for the people who live there, who feel very strongly,” Breed said. “I understand the concerns, but at the same time, everyone wants the mayor to fix the problems. I am proposing solutions, and a homeless shelter has to go somewhere. There’s one two blocks from where I live. They have to be somewhere.”

Like her continued support for safe injection sites, where drug users are offered clean equipment and supervision to prevent overdoses and direct access to addiction services, Breed said, “we need to take some risks and propose things that may make people uncomfortable” to improve street conditions and the lives of those currently living on them. Safe-injection sites have been largely sidelined in San Francisco and elsewhere in the U.S. because of legal concerns, primarily the threat of federal prosecution.

Breed isn’t likely to inspire quite the same backlash over her attempts to untangle the red tape holding back shelter and housing production. To date, she’s mandated faster review of accessory dwelling units, introduced legislation to eliminate permitting fees for affordable housing projects and plans to champion a charter amendment on the November ballot that would eliminate appeals for affordable housing and teacher-housing developments.

She described attending a ribbon-cutting ceremony for an affordable housing development in South of Market. Developing the site, she said, took 11 years.

From “the time they found the site, to the process, the permitting, the drama — enough is enough,” she said.

“We’ve piled so many laws on top we’ve put ourselves in a situation where we’re not going to be as successful unless we start getting rid of some of this stuff.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa