Illegal immigration on the southwestern border spiked 14 percent over the past year, marking the third straight increase, though Homeland Security Secretary Jeh Johnson said it was almost all because of the surge of illegal immigrant children and families from Central America — a crisis he said is subsiding.

In a broad speech on the state of border enforcement, Mr. Johnson promised more transparency from his department but challenged the press to be responsible in reporting on threats such as Ebola and the possibility of terrorists crossing the border.

He said he was not delivering “a ‘mission accomplished’ speech” and acknowledged that more needs to be done to secure the borders.

However, he said the summer flood of unaccompanied Central American children and families has fallen to rates not seen since 2012.

“The worst is over for now,” Mr. Johnson said in remarks to the Center for Strategic and International Studies.

Overall, the Border Patrol apprehended 479,377 illegal immigrants in fiscal year 2014, a jump of nearly 65,000 in one year alone and almost a 45 percent increase over the low point in 2011, when fewer than 330,000 were apprehended. Still, it’s far less than the million-plus catch recorded every year in the middle of the last decade, or the record 1.6 million illegal immigrants caught in 2000.

The number of immigrants apprehended is considered a proxy for how many are trying to cross, so an increase in apprehensions usually suggests an increase in the total getting through, too.

But the surge of illegal immigrant children may skew those calculations because they usually try to be caught, knowing the government will reunite them with relatives in the U.S. — even those residing illegally — where they have a good chance of staying for years.

The final tally of unaccompanied illegal immigrant children was 68,434, rather than the 90,000 that the Homeland Security Department predicted in the worst months of the surge.

Mr. Johnson said he is not declaring victory and that his agents will be ready for another surge should the lull prove to be a seasonal drop. His predecessor, Janet A. Napolitano, repeatedly said the border was secure, but Mr. Johnson said more needs to be done.

Still, Mr. Johnson dismissed descriptions of the border as “porous” and rejected claims that illegal immigrants or Islamic State terrorists can pass easily.

In particular, he rebutted a claim by Rep. Duncan Hunter, California Republican, that four men with ties to the Islamic State group, also known by the acronyms ISIL and ISIS, were caught coming across the border.

“In fact, these four individuals were arrested, their supposed link to terrorism was thoroughly investigated and checked, and in the end amounted to a claim by the individuals themselves that they were members of the Kurdish Workers’ Party — an organization that is actually fighting against ISIL and defended Kurdish territory in Iraq,” Mr. Johnson said. “Nevertheless, these individuals have been arrested for unlawful entry, they are detained, and they will be deported.”

President Obama is still vowing to claim executive authority to grant tentative legal status to millions of illegal immigrants already in the U.S.

Mr. Obama put off such a move this summer, saying he feared the surge of illegal immigrant children had sapped Americans’ support for his plans and could end up being a problem in the midterm elections.

Mr. Obama now has said he will act after the election but before the end of the year. Mr. Johnson on Thursday reaffirmed that president’s commitment.

“We’re developing a set of reforms — what I would characterize as comprehensive in nature but within our existing legal authority,” Mr. Johnson said.

Republicans on Capitol Hill said they were shocked that the White House acknowledged Mr. Obama delayed his decision for political reasons.

“Whether before or after the election in November, it is never acceptable for the president to re-write our laws by executive decree — the Constitution does not give him the authority to do so,” House Speaker John A. Boehner, Ohio Republican, and Judiciary Committee Chairman Bob Goodlatte, Virginia Republican, said in a joint statement Thursday. “By taking unilateral action on immigration, President Obama will inject serious constitutional questions into an already heated debate.”

Mr. Johnson detailed the massive buildup in infrastructure and manpower that has helped cut the flow of illegal immigrants: 18,127 Border Patrol agents in the Southwest, more than 400 camera systems, nearly 12,000 ground sensors, eight unmanned aerial vehicles and 353 miles of primary fencing — most of that added in the past eight years.

Mr. Johnson also promised to hire more statisticians so his department can provide an up-to-date and comprehensive picture of the border.

One of the slides he showed during his speech was the estimated number of illegal immigrants in the U.S., but he had to rely on numbers from the Pew Hispanic Center because his own department stopped putting out estimates of the illegal immigrant population more than two years ago.

Even as he promised more transparency, Mr. Johnson challenged the press to take responsibility for how it covers immigration and border issues.

He said reporters “owe the public informed, careful and responsible dialogue, not overheated rhetoric that is certain to feed the flames of fear, anxiety and suspicion.”

But the warnings often come from administration officials. Marine Corps Gen. John F. Kelly, chief of U.S. Southern Command, said this week that the surge of illegal immigrant children this summer is a harbinger of further threats, including the potential for Ebola or a crisis of refugees fleeing an outbreak in Central America.

“Sixty-eight thousand children essentially wandered across our border this year,” he said. “They get into the country pretty much unimpeded. So these populations will move to either run away from Ebola or in the fear of having been infected to get to the United States, where they’ll be taken care of.”

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