Apprehensions of illegal immigrants are up 13 percent this year, the chief of the U.S. Border Patrol testified to Congress on Wednesday as lawmakers continued to bash the Obama administration for failing to have a way of measuring how secure the borders are.

The increase in apprehensions appears to contradict the administration’s assertion that the border is more secure than ever — a claim that is critical to advocates’ hopes of passing an immigration legalization bill this year.

“We have seen an increase in attempted entries,” Border Patrol Chief Michael J. Fisher told a Senate committee.

He said part of the reason for an increase is that Congress is talking about legalizing illegal immigrants, which is luring more foreigners to try to be in the U.S. when amnesty takes effect.

All sides are searching for ways to better measure border security. Chief Fisher said the administration has been working on several yardsticks and is ready to share some of those with Congress.

That appears to be a reversal from last month, when another top Homeland Security Department official testified that the yardsticks the department was using weren’t meant to be shared with Congress or the public.

“Have you developed the metrics or not?” Sen. John McCain, Arizona Republican, demanded Wednesday, drawing an affirmative response from Chief Fisher.

“You have? You have?” Mr. McCain said. “And we’re using them?”

“We’re just starting to,” Chief Fisher replied.

The exchange highlighted one of the thorniest issues as lawmakers try to write an immigration bill this year.

The administration argues that the border is secure and that it’s time to legalize illegal immigrants. But a number of lawmakers, including Mr. McCain, say the public won’t accept legalization unless the border is considered secure enough to prevent a flood of illegal crossings into the U.S.

That is one reason why the increase in apprehension numbers is worrisome to lawmakers.

Though it appears counterintuitive, the Border Patrol says that when it catches more people crossing, that means more are crossing successfully as well. A 13 percent increase through the first half of fiscal year 2013 would represent a major step backward.

Still, lawmakers said there is little doubt border security is better than in the middle of the last decade, when millions of illegal immigrants were apprehended each year, suggesting millions more eluded capture and crossed successfully.

Sen. Thomas R. Carper, Delaware Democrat and chairman of the Homeland Security and Governmental Affairs Committee, said he sees the signs of success.

“I saw a border that I think appears to me and to a lot of other people is more secure than it’s ever been — or been in a long time,” he said.

Mr. Carper, though, said there is room to do better. He asked for a show of hands from the four administration witnesses about whether the government could do “a whole lot more” to boost border security, and all of them raised their hands.

Mr. Carper, who recently traveled to the border with Mr. McCain, said he was shocked to learn that drug cartels have taken control of mountaintops on U.S. territory and use them to direct smuggling traffic through the border.

“It blows my mind,” Mr. Carper said. “If they’re sitting on a mountaintop on Afghanistan or Iraq, I think we’d take them out.”

The eight senators working to strike a final immigration deal say they are nearing completion. Judiciary Committee Chairman Patrick J. Leahy, Vermont Democrat, on Wednesday scheduled a final major immigration hearing for next week.

Mr. Leahy said he hopes to push a bill through his committee soon after that.

Republicans argue that the Senate is moving too quickly. They have called for multiple hearings and for a long amendment process.

Opponents of legalization say that the more time voters have to study details of the bill, the less they will like it.

Mr. Leahy, though, said these issues have been simmering for years, his committee already has held several hearings this year, and there is no need for a drawn-out process.

“Our hearings have informed the Senate and the public of the various and pressing needs to reform the nation’s broken immigration system,” he said. “I look forward to continuing that discussion next week as we head toward marking up legislation with deliberation and openness.”

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