Lawmakers, shooting victims and advocates for stricter gun laws including actor Matthew McConaughey spoke out in Washington on Tuesday for legislation to reduce mass shootings amid signs of movement on an issue that has stymied Congress for years.

Democrats in the US Senate said they were encouraged by ongoing talks with Republicans. The White House said President Joe Biden simply wanted to see some kind of legislation passed, even if a deal could not be reached on his call to ban assault rifles, as Congress debates federal gun legislation after more than a decade of inaction on the issue.

The renewed push to...