WASHINGTON — The Obama administration has released into the US an untold number of immigrant families caught traveling illegally from Central America in recent months and although the government knows how many it’s released, it won’t say publicly.

Senior US officials directly familiar with the issue, including at the Homeland Security Department and White House, have so far dodged the answer on at least seven occasions over two weeks, alternately saying that they did not know the figure or didn’t have it immediately at hand. “We will get back to you,” the Homeland Security deputy secretary said Friday.

The figure is widely believed to exceed 40,000 since October. It’s believed to be slightly below the roughly 52,000 children caught traveling illegally from Central America over the same period, an extraordinary increase since last year that is driving a humanitarian crisis at the border.

Despite promises to the contrary, this is how it looks when the image-conscious Obama administration doesn’t want to reveal politically sensitive information that could influence an important policy debate. The mystery figure is significant because the number of families caught crossing from Central America represents a large share of new immigration cases that will further strain the overwhelmed US immigration courts system. It also affects federal enforcement strategy, such as where to deploy the border patrol, and political calculations about whether Congress or the White House will relax American immigration laws or regulations before upcoming congressional elections in November.

Most of the immigrant families are from Honduras, El Salvador or Guatemala and cannot be immediately repatriated, so the government has been releasing them into the US interior and telling them to report within 15 days to the nearest US Immigration and Customs Enforcement offices. Despite promises for better transparency on immigration issues, the administration has been unwilling to say how many immigrant families it’s released or how many of those subsequently reported back to the government after 15 days as directed.

The government has limited options for detaining families caught crossing the border illegally, usually mothers with children. It has space for fewer than 100 family members at its only detention center for them, in Berks County, Pennsylvania. The administration announced Friday that it will open new detention facilities for immigrant families, including a 700-bed facility at the Federal Law Enforcement Training Center in Artesia, New Mexico, which is home to the Border Patrol’s training academy. It didn’t say when that new immigration jail would open or how many others it will build.

The administration did not immediately respond Monday to renewed questions about why it won’t reveal the figure.

Here are details of at least seven occasions since June 9 when senior US officials declined to say how many immigrant families the government has released in recent months:

June 9: A senior administration official, speaking on condition of anonymity during a conference call, told reporters there was no information available about the number of adults with children who were released.

June 10: On Capitol Hill for a congressional briefing, Homeland Security Secretary Jeh Johnson told an Associated Press reporter in response to a question about the figure: “I have no news for you.” He urged AP to ask the department’s public affairs office, which did not answer roughly a dozen requests for the information.

June 12: At a news conference about immigration, the Homeland Security secretary did not respond to a shouted question about the number of immigrants released.

June 13: The Customs and Border Protection commissioner, Gil Kerlikowske, told the AP that he didn’t know how many immigrants his agency released. He said the administration was compiling the data.

June 13: During a visit to Chicago, Johnson told the AP he didn’t have the information with him.

Friday: On a conference call, the Homeland Security deputy secretary, Alejandro Mayorkas, said, “We will get back to you with respect to the precise numbers on the notices to appear.” He added later: “I don’t have the response to the data question that you asked.”

Friday: When reporters asked White House press secretary Josh Earnest about the releases during a news conference, he responded: “I don’t have those numbers here … but what I do have is a clear commitment from this administration to deal with what is an emerging humanitarian situation.”