WASHINGTON — The Department of Homeland Security is finalizing a proposal to collect fingerprints or eye scans from all foreign travelers at U.S. airports as they leave the country, officials said, a costly screening program that airlines have opposed.

The plan, which would take effect within two years, would collect fingerprints at airport security checkpoints, departure gates or terminal kiosks, allowing the government to track when roughly 35 million foreign visitors a year leave the country and who might be overstaying their visas, DHS officials said.

The department plans to send the proposal to the White House as soon as next month for review and inclusion in President Barack Obama's next budget.

Some experts and former government officials are skeptical. In a concession to industry, DHS said it probably will drop plans to require airlines to pay for the bulk of the program and is looking to cut costs, which could reach $1 billion to $2 billion over a decade, largely to be paid by taxpayers or foreign travelers. In addition, the program would not operate for now at land borders, where 80 percent of noncitizens enter and leave the country, because fingerprinting travelers there could cost billions more and significantly delay commerce.

The ultimate scope of the system — how rigorous it is and its final price tag — will signal how the Obama administration and a Democratic Congress balance expensive post-9/11 security mandates against the nation's financial constraints, analysts and former government officials said. Congress might have to re-examine the value of border controls that a few years ago were deemed critical for security and for curbing illegal immigration but that might be less effective than first thought or carry unpopular economic or diplomatic costs, they added.

"It will be up to Congress to put its money where its mandate is," a senior DHS official said, outlining the plans on condition of anonymity because Secretary Janet Napolitano has not made a final decision. "The administration and Congress have to decide how they want to implement this in times of budget austerity."

Sen. Dianne Feinstein, D-Calif., a prominent congressional supporter of the tracking requirement, said she was pleased with DHS's "long overdue" move.

"A biometric exit system is critical to tracking the arrival and departure of foreign nationals — not just through a paper trail, but through fingerprints, photographs, and other fraud-proof biometric identifiers," Feinstein said in an e-mail statement.