The Kentucky Republican's "Trust but Verify" measure was tabled on a 61-37 vote, The Hill reported.
The amendment would have required Congress to vote on whether border security measures were being enforced before immigrants would be granted legal status, the Washington publication said. The measure also would have required completion of a border fence in five years and provided that no national identification card system be established.
The House Judiciary Committee Tuesday night voted 20-15 along party lines to approve its first immigration bill, a proposal that would increase enforcement and border security, The Hill reported.
The Strengthen and Fortify Enforcement Act, or SAFE Act, is one of several bills Chairman Bob Goodlatte, R-Va., said the committee will send to the House floor in the coming weeks. He has said he prefers to tackle immigration reform with a series of smaller bills rather than one sweeping bill as the Senate is doing.
"The SAFE Act maintains the integrity of our immigration system by granting states and local governments the authority to enforce federal immigration laws," Goodlatte said in a statement.
"The bill also strengthens national security and protects our communities from those who wish to cause us harm. While more work has yet to be done, today's approval of the SAFE Act brings us one step closer to solving the immigration puzzle," he said.
"We have, and will continue, to take a step-by-step approach to immigration reform, thoroughly examining each piece in detail and working to find consensus on the other issues we need to fix."
The committee's schedule Wednesday included consideration of legislation to create an agricultural guest-worker program, The Hill said.
Rep. Zoe Lofgren, D-Calif., who has been negotiating on a separate bipartisan immigration bill, said the Republican-backed bill "takes us back in time to an approach that has long been rejected by the American people."