"I'm not going to rest until I see something happen. We've got to have our legislators and congressmen step up to the plate and stop being cowards about this," Parker told CNN, describing himself as a supporter of the constitutional right to keep and bear arms.
He said the National Rifle Association, the powerful U.S. gun lobby, likely would contend that his daughter and Ward would have been safe if they themselves had been armed.
"It wouldn't have made any difference," Parker said. "How many Alisons is this going to happen to before we stop it?"
The United States had about 34,000 firearms deaths in 2013, with almost two-thirds of them suicides, according to the Centers for Disease Control and Prevention.
Sarah Trumble, a senior policy counsel for the Third Way, a Washington think tank, said prospects for gun control had little chance in the Republican-controlled Congress, despite intense media focus on the Virginia killings.
"There's no playbook for what to do here," she said, but added that changes were more likely in states than at a federal level. "The states are really where the action is."
The last time there was a push at the federal level for tighter gun control was following the massacre of 26 people, mostly children, at the Sandy Hook elementary school in Newtown, Connecticut, in December 2012.
President Barack Obama supported legislation that would have extended background checks for gun buyers and banned rapid-firing assault weapons. But despite national revulsion over the Newtown killings, it was rejected in April 2013 by the U.S. Senate, including by some lawmakers in Obama's Democratic Party.
After Wednesday's shooting, Obama reiterated his frustration over the issue of gun violence, saying the United States needs to do "a better job of making sure that people who have problems, people who shouldn't have guns, don't have them."