The federal government wants to issue more visas for foreign workers to take temporary jobs in housekeeping, landscaping and other fields \u2014 even as President Trump seeks to seal off the border with Mexico, where most of those workers come from. The Departments of Homeland Security and Labor said they planned to issue up to 30,000 additional H-2B visas through Sept. 30, the end of the federal fiscal year. Congress has generally capped the number of visas, which businesses compete for, at 66,000, divided evenly between summer and winter seasons. Only workers who had previously secured the visas would be eligible for the proposed additional ones. The visas provide legal status for immigrants in temporary nonfarm jobs with landscaping companies, restaurants, hotels and amusement parks, among other industries. Last fiscal year, about 75 percent of these visas were issued to workers from Mexico, according to State Department data. Visas were also issued to, among others, Jamaicans, Guatemalans and South Africans. Business groups regularly push lawmakers to raise or eliminate the cap on the number of visas issued, a demand that has increased as unemployment has dropped and domestic workers have become more scarce. The government\u2019s move to expand the H-2B program appeared inconsistent with the Trump administration\u2019s repeated message about a crisis on the southwestern border of the United States. On Saturday, Mr. Trump told a gathering of the Republican Jewish Coalition that \u201cour country\u2019s full.\u201d \u201cWhat can we do? We can\u2019t handle any more,\u201d he said. \u201cOur country\u2019s full. You can\u2019t come in, I\u2019m sorry.\u201d Alex Nowrasteh, a senior immigration analyst with the Cato Institute, a libertarian think tank, said there were \u201ca lot of contradictions\u201d within the government\u2019s proposals. \u201cOn one hand, we need more people because the economy is booming,\u201d he said. \u201cThen on the other hand, to say, \u2018The country is full, go back\u2019 \u2014 it\u2019s impossible to reconcile those.\u201d The H-2B visa program, which started in the mid-20th century, has been a feature of a persistent debate over using foreign workers for seasonal labor. Unions and immigration opponents argue that hiring H-2B workers suppresses wages and deprives Americans of jobs. Advocacy groups say foreign workers are often exploited, and employers say the cap encourages businesses to hire undocumented workers. Andrea Palermo, a spokeswoman for the Department of Homeland Security, did not directly answer questions about what was behind the plan for additional H-2B visas. She also did not address questions about the apparent contradiction in the administration\u2019s positions. \u201cCongress \u2014 not D.H.S. \u2014 should be responsible for determining whether the annual numerical limitations for H-2B workers set by Congress need to be modified, and by how much, and for setting parameters to ensure that enough workers are available to meet employers\u2019 temporary needs throughout the year,\u201d she said. The White House did not immediately respond to requests for comment on Sunday. Mr. Nowrasteh said he favored the H-2B program. \u201cI think the economic benefits from the H-2B visa are very large, the benefits to the workers are huge,\u201d he said. Because businesses are required to show that no American workers want the jobs, the cap \u201cmakes no sense,\u201d he said. \u201cIf they try to hire Americans, and Americans don\u2019t want to do that job, then there should be no cap,\u201d he said. Mr. Nowrasteh said he believed that H-2B visas for Mexican workers have helped drive down illegal immigration. He said expanding the program or eliminating the cap could also help reduce the number of undocumented immigrants from Central American countries. Last month a bipartisan group of senators, led by Susan M. Collins and Angus S. King of Maine, asked the Department of Homeland Security to increase the number of visas as a way to support small businesses in a tight labor market, especially those preparing for the summer season. \u201cIn the short run, many areas of our country simply lack the working-age population needed to meet the demand for seasonal jobs,\u201d the senators wrote in a letter signed by 11 lawmakers. \u201cIn some industries, particularly tourism, we fear that the demand for workers so far outstrips the available supply that businesses could be forced to curtail operations, putting at risk the jobs of American workers who fill year-round positions at these establishments.\u201d But Mark Krikorian, the executive director of the Center for Immigration Studies, which supports curbs on immigration, was critical of the program and said it enabled \u201cbusinesses to avoid hiring people they\u2019d rather not hire.\u201d \u201cA nation with a third of a billion spanning an entire continent, with 50 million working-age people not in the labor force, doesn\u2019t need to be importing labor,\u201d he said. Mr. Krikorian said the proposed expansion of the program was not \u201cbacktracking or flip-flopping\u201d by the administration. \u201cThe president has always been a big fan of these guest worker visas,\u201d said Mr. Krikorian, who noted that Mr. Trump\u2019s properties, such as Mar-a-Lago, use this visa program to hire workers.