Labor and business leaders have agreed in principle on the details of a new visa program for low-skilled foreign workers, clearing the last major hurdle for a bipartisan Senate proposal to overhaul the nation’s immigration laws, a person involved in the negotiations said Saturday.

The agreement came late Friday after several days of negotiations between the U.S. Chamber of Commerce and the AFL-CIO, the country’s largest labor organization, as well as the eight senators involved in drafting the comprehensive immigration bill.

The two sides agreed on how to overcome the final sticking points, including how much the foreign workers would be paid and which industries would be exempt from the guest-worker program. Final approval came in a phone call Friday night arranged by Sen. Charles E. Schumer (D-N.Y.) with Chamber president Thomas Donohue and AFL-CIO head Richard Trumka, said the person involved in the talks, who spoke on the condition of anonymity to discuss private deliberations.

Trumka said in a statement Saturday night: “We have created a new model, a modern visa system that includes both a bureau to collect and analyze labor market data, as well as significant worker protections.” He also reiterated the AFL-CIO’s support for the overall reform effort, including the path to citizenship for undocumented migrants.

But the complexity of the matter was highlighted when one member of the business community said Saturday afternoon that the lead negotiators on the business side had not seen written details of a final agreement and cautioned that declaring the matter resolved was premature.

“Business groups are still waiting to see the details. I don’t know where it’s coming from,” the business official said, speaking on the condition of anonymity because of the sensitivity of the negotiations. “I don’t want to blow this up at all, but to say everyone’s signed off on this is getting ahead of ourselves.”

Members of the Senate working group also declined to confirm the deal. Alex Conant, a spokesman for Sen. Marco Rubio (R-Fla.), wrote on his Twitter account, “Senate negotiators are making good progress on immigration reform, but we’re not done yet.”

A spokesman for Sen. John McCain (R-Ariz.) declined to comment Saturday.

The person who disclosed the guest-worker deal said that all eight senators had not formally signed off on the terms but said that could happen over the next few days because all had been briefed at each stage of the talks.

The guest-worker dispute was considered the final major impasse that threatened to delay the immigration bill that the Senate working group hopes to unveil in the second week of April. Senate aides, who will begin writing the hundreds of pages of legislation this week, cautioned that nothing in the deal is final until the four Democrats and four Republicans in the group have agreed to all portions of the written document.

In addition to the guest-worker program, the Senate bill will feature a 13-year path to citizenship for illegal immigrants, increases in the number of visas for highly skilled tech workers, elimination of some categories of family visas and increases in border control and workplace security, people familiar with the talks have said.

Though a number of smaller points are unresolved, Senate aides said they are hopeful that a bill can be introduced in the Judiciary Committee in time to be moved onto the Senate floor by Memorial Day. The goal would be to have a vote of the full Senate by the August recess, the aides said. The House has a proposal developed by its own bipartisan group that also could be unveiled in the next few weeks.

President Obama, who has made immigration reform the top priority of his second term, has said he hopes to sign a comprehensive bill this year. In 2007, a dispute between business and labor over a guest-worker provision helped sink a bipartisan immigration bill in the Senate. The president has not taken a position on a guest-worker program this year.

According to the person who disclosed the guest-worker deal, Schumer called White House Chief of Staff Denis McDonough to inform him of the deal. The administration had mostly remained out of the daily negotiations as business and labor tried to work out the deal under the Senate’s guidance.

A White House spokesman said in a statement Saturday that the president “continues to be encouraged by progress being made by the bipartisan group of Senators,” adding, “We look forward to seeing language once it is introduced, and expect legislation to move forward as soon as possible.”

Businesses had lobbied for 400,000 new visas under the new program, but labor unions wanted far fewer because of concerns that such a system would negatively affect wages and benefits for American workers.

Under the Senate’s proposal, businesses would be allowed starting in April 2015 to hire 20,000 foreign workers for low-skilled jobs in a new “W visa” program — the number rising to 75,000 in 2019, according to people familiar with the details.

After that, the number would rise and fall each year depending on recommendations from a new “Bureau of Immigration and Labor Market Research,” which would analyze employment data. Those familiar with the talks said it would take many years before the visa program would approach the annual proposed cap of 200,000 foreign workers.

Meanwhile, construction industries would be limited to no more than 15,000 visas annually and would be banned from hiring any foreign guest workers for more highly skilled technical jobs such as electrician positions.

The Chamber and AFL-CIO agreed to a wage scale that would pay foreigners the greater of actual or prevailing wages. It would be based partly on a formula that takes into account actual wages paid by the employer to similarly situated U.S. workers, as well as regional and industry scales.

Companies, except in the construction industry, could hire workers beyond the annual caps if they were willing to pay significantly higher wages.

Union officials declined to comment Saturday. Blair Latoff Holmes, a spokeswoman for the Chamber, confirmed that Schumer and Donohue spoke Friday but said she did not know whether Donohue had spoken with Trumka. She declined to comment on whether a deal had been reached.

“The senators will make the decisions about any final agreements and what makes the best public policy overall,” Holmes said in an e-mail.

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