A day after the deadliest US mass shooting this year in which 12 people were shot dead at a government building, Elizabeth Warren was asked what she would do to confront an “overwhelming surge” in such events.

The Massachusetts senator said she wanted to reframe the question, then continued: “It’s not just mass shootings.” Every day in America, she said, gun violence occurs “on sidewalks and playgrounds and people’s backyards. It’s happening family by family across the country. And it doesn’t get the same headlines. And that is wrong.”

In San Francisco on Saturday, Warren was one of 14 candidates for the presidential nomination appearing at the California Democratic convention, seeking to pitch to progressive voters.

Her response, delivered at a “Big Ideas” forum hosted by the progressive group MoveOn, echoed what activists of color have argued for years: that the US gun control debate focuses too much on mass shootings and ignores the daily toll of gun violence, which disproportionately affects black and brown Americans.

All the frontrunners for the Democratic nomination were in California, except Joe Biden, who was in Ohio. In all, 14 candidates converged, making this the largest gathering so far of 2020 hopefuls.

For Democrats, endorsing stricter gun control laws is no longer a brave move. It is now a standard part of the policy agenda. In her answer, Warren endorsed ideas that are familiar across the sprawling 2020 field: expanding background checks on gun sales, banning military-style weapons, investing more in scientific research on gun safety.

But Warren’s decision to push back against the focus on “mass shootings” did not just reflect a conversation among activists who have increasingly criticized racial disparities in the way politicians address gun violence. It also echoed arguments made by survivors of last year’s school shooting in Parkland, Florida: that the fact shootings in suburban schools get more attention than daily killings of children of color is “wrong”.

Many of the candidates emphasized that their “big ideas” were relevant to racial justice, from the New Jersey senator Cory Booker’s argument that his proposal to create “baby bond” savings accounts for every American child would help erase the wealth gap, to New York senator Kirsten Gillibrand’s argument that her national paid family leave plan would particularly benefit women of color.

Both Gillibrand and former Texas congressman Beto O’Rourke told the audience they supported legislation to establish a formal process for considering whether black Americans should receive reparations for slavery.

Such a move would “squarely confront the legacy of slavery and segregation and Jim Crow,” O’Rourke said, calling it “fundamental to any repairs of the damage that we have caused”.

In a response to a question, O’Rourke also acknowledged the advantages he had as a white male candidate.

“There are advantages that I brought into this race that I did not earn,” he said, “that were functions of circumstances and fortunate and fate, being born a white man in this country.”

In general, the candidates made clear that they think the 2020 election should be about more than just attacking Donald Trump. Booker, for example, was cheered for saying the election “should not be just getting one guy out of office, we should have bigger aspirations than that”.

Among his big ideas was a pledge to make sure that “social media platforms do not become platforms for hate and bigotry”. If he is elected president, he said, his Department of Justice will put real resources into investigating white supremacist terrorism.

The Vermont senator Bernie Sanders promised to “stop endless wars” and to work with other countries to end the world’s reliance on fossil fuels, rather than spending trillions on “weapons of destruction to kill each other”.