The Senate Judiciary Committee is considering 300 amendments that could reshape or potentially derail the massive bill, The New York Times said.
"We know there are many who want to kill this bill," said Sen. Charles Schumer, D-N.Y., in opening remarks. Schumer, one of the co-authors of the bill, urged colleagues, however, to "be constructive."
Sen. Patrick J. Leahy, D-Vt., chairman of the committee, has made all of the amendments publicly available on the committee's website.
Sen. Richard Durbin, D-Ill., said the bill, which implements stricter border security while providing a route to to citizenship for the nation's 11 million undocumented immigrants, gives lawmakers the chance to "write an immigration bill for the 21st century, for America and its future."
One of the measures adopted Thursday requires the secretary of homeland security to report to the Senate and House Judiciary Committees on how the border security strategy is being implemented.
Sen. Charles E. Grassley, R-Iowa, the ranking Republican on the committee, has said he wants to make sure the public understands what is contained within the 867-page bill.
"I want to know how the bill doesn't repeat the mistakes of our past. I want to know how it will benefit generations for years to come. And, I want to know how the bill preserves the rule of law," he said in a statement. "Since we only do comprehensive immigration reform once every 25 years or so, we have to get it right."
Grassley has proposed 77 of the 300 proposed changes to the bill. One of the measures, approved Thursday, would require continuous surveillance of 100 percent of the U.S. border and 90 percent effectiveness of enforcement of the entire border, the Times said.
The committee also approved an amendment that prohibits border crossing fees.
Lawmakers rejected by a 6-12 vote a proposed amendment that would have required "effective control" of the U.S. southern border before allowing illegal immigrants to apply for registered provisional status, Politico said.