* Iowa's Grassley warm to school security, anti-trafficking plans
* For proposed ban on "assault" weapons, another hurdle
* Senate Judiciary Committee takes up four bills on Thursday
By Thomas Ferraro
WASHINGTON, March 5 (Reuters) - The top Republican on the Democrat-led U.S. Senate Judiciary Committee said on Tuesday that he may back at least two of the four gun-control bills that the panel will consider this week.
Iowa Senator Charles Grassley's support could help both measures - one aimed at cracking down on illegal gun trafficking, the other designed to bolster security at schools - pass the Senate.
But Grassley, echoing many other Republicans in Congress, said he would not support a plan to renew a ban on the sale of military-style, semi-automatic "assault" weapons.
Grassley's reluctance to embrace the assault weapons ban - and his hesitance on another measure that would expand background checks on prospective gun buyers - reflect the difficulty that Democrats are likely to face in getting a comprehensive gun-control package through Congress.
President Barack Obama has backed a range of proposals aimed at reducing gun violence, a cause that has taken on greater urgency since 20 children and six adults were killed by a gunman at a Connecticut school in December.
Grassley and other Republicans say that the most controversial proposal - reviving the federal ban on the sale of assault weapons that was in effect for a decade before expiring in 2004 - amounts to a violation of Americans' constitutional right to bear arms.
"That bill isn't going anywhere," Grassley told Reuters, voicing the sentiment of many on both sides of Washington's political divide.
Grassley said he is undecided about the bill that would require criminal and mental-health background checks of all gun buyers. Currently, 40 percent of buyers are not screened, mostly involving sales among private individuals.
The Judiciary Committee, with 10 Democrats and eight Republicans, will consider the four gun-control bills on Thursday, and amendments to them are likely. All four are expected to be reported out of committee and sent to the full Senate.
CONCERNS ABOUT REGISTRATION
Four senators - Democrats Charles Schumer of New York and Joe Manchin of West Virginia, and Republicans Tom Coburn of Oklahoma and Mark Kirk of Illinois - have been working on a background-check bill for weeks. But they have not been able to reach a compromise on how records of gun sales should be handled.
Democrats say that a record of private sales, which would show whether a background check was conducted, must be kept to be able to enforce the proposed new law.
But Coburn fears that such records could clear the way to registration of guns, which gun-rights groups have long opposed, a senior Senate aide said.
"Everyone is scared of this stuff leading to registration," Grassley said.
Even so, he said, "There might be something done on background checks." He said he needed to talk further with colleagues before making a decision.
If there is no bipartisan agreement on background checks, Schumer may offer a bill that has no Republican co-sponsors and would require record-keeping of private gun sales, a Senate aide said.
Such a bill could face a possible Republican roadblock that would require 60 votes to clear in the 100-member Senate. Democrats control the chamber, 55-45.
Grassley said he may back a bill offered by Democratic Senator Barbara Boxer of California to bolster school security - if she agrees to cut its cost.
"Her bill could become a bipartisan bill," Grassley said.
Boxer said that in response to Grassley's complaints, she had decided to slash the proposed annual cost from $100 million to $40 million.
Separately, Republican Senator Lindsey Graham of South Carolina and Democratic Senator Mark Begich of Alaska plan to offer a bill on Wednesday aimed at providing better treatment for the mentally ill and keeping them from getting firearms, aides said. (Editing by David Lindsey and Philip Barbara)