The House Judiciary Committee will not include a universal background check system in legislation it produces to reduce gun violence, the panel’s chairman, Rep. Bob Goodlatte (R-Va.), said Wednesday.

Goodlatte told reporters that his committee would focus on cracking down on illegal firearms and improving the existing check system. But he said he did not support “universal” background checks because of concerns that they would lead to a national gun registry, which critics have argued would represent an invasion of privacy for law-abiding gun owners.

“The fact of the matter is, we need to look at all of these issues, but I think where we’re going to find the ability to produce legislation is going to be focused on two things primarily,” the chairman said at a breakfast sponsored by the Christian Science Monitor. “One is improving the background check system, but universal background checks I do not think will be part of that.”

Goodlatte’s opposition throws a wrench into a central piece of the Obama administration’s plan for reducing gun violence following the massacre in Newtown, Conn., and other recent mass shootings.