Rome (CNN) — Two aid workers rescued in a U.S. military raid in Somalia need time out of the media spotlight to decompress and recover, the military said Friday, in outlining key steps in the reintegration process for the former captives.

Jessica Buchanan and Poul Thisted arrived at a U.S. base in Sicily Thursday, a day after being freed in Somalia.

Their health and welfare are the top priority, the military statement said, as it appealed for the media to respect the privacy of the freed hostages and their families.

“It is extremely important that they have the chance to decompress from this event without the pressure of instant overwhelming public notoriety,” it said.

The families of Buchanan and Thisted expressed their relief that they were rescued unharmed in a joint statement Friday, issued through the Danish Refugee Council, the agency for which the pair worked.

“We are grateful for all the efforts that have been put into getting them safely back to us and for the fact that a very difficult chapter in our lives is over,” it said.

“We need to look ahead now, and it is going to take time for us all to adjust and to return to normal life. We would like to thank all media for having respected our needs for privacy, and we request for everyone to continue to show us this respect and to give us time and privacy, which is all we need now.”

Daring mission saves aid workers

The reintegration process allows the U.S. Defense Department to gather critical information while taking care of the freed captives, the military said.

“Reintegration and decompression also allow returnees to resume stable professional, family, and community activities with minimal complications.

“The process ensures returnees have the best chance to return to their previous lives following this significant event.”

The two hostages were freed in a dramatic overnight rescue operation.

U.S. special operations forces parachuted into Somalia from airplanes in the early hours of Wednesday morning, advanced on foot to a compound where the two kidnapped international aid workers were being held and freed them, U.S. officials said.

The nine gunmen holding the hostages were killed, the officials said.

The kidnappers seized Buchanan, 32, and Thisted, 60, on October 25 in the central Somali town of Galkayo after they visited humanitarian projects there, said the Danish Refugee Council, the agency for which they work. Neither was harmed, the aid group said.

Buchanan’s father, John, was to go to Sicily to see her, CNN learned. She is not in custody and can leave when she wants but, if she stays, when ready she will be returned to the United States, probably in a U.S. military aircraft.

Somalia’s transitional government welcomed the U.S. military operation Thursday.

The rescue of the aid workers “is a great joy to the Somali government and to all Somalis as well as to all right thinking people everywhere,” the government said in a statement.

“Hitting them hard is the only language kidnappers of innocent people, pirates and terrorists understand, and every opportunity should be taken to wipe out this scourge from our country,” the government said.

The new United Nations envoy to Somalia — the first permanent U.N. representative there in 17 years — also expressed understanding about the military operation.

“If negotiations fail, all means must be applied, including rescue operations,” Augustine Mahiga said Thursday, even as he urged that lives be protected “on both sides.”

Thisted’s sister and brother-in-law wept for joy when they heard he had been rescued, the brother-in-law, Svend Rask, told Denmark’s TV2.

“She was overjoyed when she told us what happened,” Rask said, speaking of the daughter who gave them the news.

The Navy SEAL unit that killed al Qaeda leader Osama bin Laden last year in Pakistan participated in the rescue mission, a U.S. official said, without specifying whether any of the same individuals were on both assaults.

The SEALs are part of the Naval Special Warfare Development Group, formerly known as SEAL Team Six.

Pentagon spokesman George Little said the rescue team included special operations troops from different branches of the military, but he would not specify the branches.

The area where the hostages were seized is known as a hub for pirates, rather than an area of Islamic militant activity.

A number of high-profile abductions of foreigners have occurred in Somalia and in Kenya, close to the largely lawless Somali border.

Somalia Report, a website that tracks piracy statistics, said over $ 150 million was paid out in ransoms in 2011.

Successful pirate attacks on merchant vessels began to drop off in 2011 in face of improved shipping security — including on board armed security detachments — and stronger action from the foreign navies patrolling the Gulf of Aden and Indian Ocean.

The International Maritime Bureau, which tracks piracy, said the number of attacks had risen but the success rate had plummeted to 12% in the first nine months of 2011.

The aid workers were part of the Danish Refugee Council’s de-mining unit, which aims to make civilians safe from land mines and unexploded ordnance.

Buchanan has been employed as a regional education adviser with the mine clearance unit of DRC since May; Thisted, a community safety manager with the de-mining unit, has been working in Somaliland and Somalia since June 2009.

CNN’s Livia Borghese contributed to this report.