WASHINGTON—The Senate Judiciary Committee seems all but certain to start voting on an assault weapons ban and other gun curbs next week, Congress' first roll calls in response to the Newtown, Conn., slayings of 26 students and staff at an elementary school in December.

The Democratic-written bills largely follow President Barack Obama's proposals for limiting gun violence, which have been opposed by the National Rifle Association and generated little support from congressional Republicans.

Sen. Patrick Leahy, D-Vt., the committee chairman, said Monday that the panel would consider:

—A bill by Sen. Dianne Feinstein, D-Calif., banning assault weapons and ammunition magazines holding more than 10 rounds;

—A Leahy measure toughening federal penalties for illegal trafficking of guns, including up to 30-year sentences for people buying firearms they know will be used in crimes;

—A measure by Sen. Barbara Boxer, D-Calif., increasing federal grants for school safety measures such as installing surveillance equipment.

Leahy said the panel would also consider still evolving legislation expanding the requirement for federal background checks for gun purchases, which are now required only for transactions by federally licensed gun dealers. Requiring those checks for nearly all gun sales is a top Obama goal, and one that has received the broadest support by the public and in Congress.

The details of the bill are not yet complete as liberal Sen. Charles Schumer of New York, the No. 3 Senate Democratic leader, continues trying to reach a compromise with conservative Sen. Tom Coburn, R-Okla.

Leahy announced plans for the panel to start voting on the measures this Thursday. But committee rules let senators postpone announced legislative work for a week, a practice that is followed routinely. The panel's top Republican, Sen. Charles Grassley of Iowa, said he would request that delay.

"It's just a process of making sure we have plenty of time to study" legislation, Grassley said in a brief interview.

Feinstein is chairing a Judiciary Committee hearing on Wednesday on her effort to ban assault weapons, a proposal that is given low odds of enactment because of opposition by many Republicans and resistance by some moderate Democrats.

Witnesses are to include Neil Heslin of Newtown, whose 6-year-old son, Jesse, was killed at the school and Dr. William Begg, an emergency room physician in Newtown who helped treat victims that day. Feinstein has said the public needs to know how gruesome assault weapons wounds can be.