New York (CNN) -- Information taken from Osama bin Laden's compound in Pakistan indicates that al Qaeda was mulling attacks on a handful of U.S. cities, timed to significant dates, a U.S. official said.

One law enforcement source said that an alert issued Thursday and tied to rail security is the first new notice that can be linked to the early Monday raid on the Abbottabad compound where the al Qaeda leader was found and killed.

More details emerge about the raid

That notice says that, in February 2010, al Qaeda members discussed a plan to derail trains in the United States by placing obstructions on tracks over bridges and valleys.

The plan was to be executed later this year, coinciding with the 10th anniversary of the September 11, 2001, attacks. But no specific city or rail system was identified in the notice.

"It is not surprising that we would find this kind of information in the home of the world's most wanted terrorist," said one U.S. official.

The federal department confirmed the notice went out to federal, state, local and tribal authorities, with spokesman Matt Chandler stressing that "this alleged al Qaeda plotting is based on initial reporting, which is often misleading or inaccurate and subject to change."

"We have no information of any imminent terrorist threat to the U.S. rail sector, but wanted to make our partners aware of the alleged plotting; it is unclear if any further planning has been conducted since February of last year," Chandler said.

Material gathered from the same compound also suggests that al Qaeda was particularly interested in striking Washington, New York, Los Angeles and Chicago, according to the official.

U.S. authorities have found that al Qaeda appears especially interested in striking on significant dates like July 4, Christmas and the opening day of the United Nations.

These threats come days after U.S. commandos were helicoptered into a northern Pakistan housing compound, where they killed bin Laden and four others, then took off with his body and numerous materials.

Osama's wife: We lived there 5 years

The cache included audio and video equipment, suggesting bin Laden may have taped makeshift messages there, a U.S. official said. Ten hard drives, five computers and more than 100 storage devices, such as disks and thumb drives, were also found, a senior U.S. official told CNN. Commandos also recovered five cell phones, paper documents and five guns, including AK-47s and pistols.

Earlier Thursday, a U.S. official speaking to CNN on condition of anonymity said that "valuable information has been gleaned already," though no specific plots or terrorist suspects were identified.

Members of the U.S. special operations unit involved in that raid will meet with President Barack Obama on Friday, a senior administration official said Thursday.

Obama will travel to Fort Campbell in Kentucky on Friday "to privately thank some of the special operators involved in the operation," according to the official. On Wednesday, the president met at the White House with Adm. William McRaven, the head of the Joint Special Operations Command "to thank him personally."

More details, meanwhile, emerged Thursday about the operation engineered and executed by this team, according to a U.S. official with knowledge of debriefings from Navy SEALs involved.

The raid occurred in a span of 38 minutes early Monday morning, following CIA reports of repeated sightings of a tall man doing "prison yard walks" around the yard of the housing compound in Abbottabad, which was under constant surveillance, this official said. U.S. authorities never definitely determined beforehand that the man was in fact bin Laden, but they eventually concluded that there was enough evidence to go through with the operation.

The first man killed in the mission -- which this official said was code-named "Operation Neptune Spear" -- was the Kuwaiti courier who had worked for bin Laden. He was shot dead after a brief gunfight in a guest house. From that point on, it is now believed no other shots were fired at the U.S. forces, the official said -- which contrasts to earlier U.S. government reports describing the operation as a "firefight."

The troops then moved into the compound's main three-story building, where they shot and killed the courier's brother. As they went upstairs and around barricades, one of bin Laden's sons rushed at them and was subsequently killed, according to this latest account. Neither of these men had weapons either on them or nearby, this official said.

The U.S. official said that the team then entered the third-floor room where bin Laden was, along with his Yemeni wife and several young children. The al Qaeda leader was moving, possibly toward one of the weapons that were in the room, when he was shot, first in the chest and then in the head. He never had a gun in hand but, like the other men, posed an imminent threat, according to the U.S. official.

An unidentified woman also was killed.

Afterward, one SEAL lay down beside the dead bin Laden to measure his height and further determine that he, in fact, was the man who for years has ranked atop the FBI's "Most Wanted Terrorists" list. He had 500 euros (about $745) in cash and two telephone numbers sewn into his clothing when he was killed, a congressional source present at a classified briefing on the operation told CNN Wednesday.

While the Friday meetings will focus on this raid, Thursday was about those personally affected by followers of bin Laden, when they turned hijacked jetliners filled with fuel and passengers into missiles aimed at New York and Washington.

Nearly 3,000 people were killed in the September 11, 2001, attacks. The vast majority of the victims were killed when two hijacked planes crashed into the twin towers of the World Trade Center, causing them to collapse. A third plane crashed into the Pentagon outside Washington, killing 184 people, plus the five hijackers. The fourth hijacked jetliner was heading for a target in Washington when it crashed in a field near Shanksville, Pennsylvania, after passengers rushed to take control of the plane. Forty passengers and crew, not including the four hijackers, died in that crash.

Obama attended a wreath-laying ceremony and took part in a moment of silence at the latter site, which is now being rebuilt. The president also had lunch Thursday at the home of Engine Company 54, which lost 15 members in the towers' collapse.

The U.S. Navy SEAL team that killed bin Laden "were doing it in the name of your brothers that were lost," Obama told the firefighters.

"It's some comfort, I hope, to all of you to know that when those guys took those extraordinary risks going into Pakistan, that they were doing it in part because of the sacrifices that were made in the States," he said on his way into the firehouse.

Obama's meetings with firefighters were private exchanges, during which the president sought to mark the end of the nearly decade-long manhunt.

"Coming by was really a spectacular thing, you know," firefighter Joe Ceravolo told reporters after Obama's visit. "We just wanted to tell him we thank him for what he did on Sunday, and all the troops and all. We want to let them know that we're with them every step of the way, and God bless them. I mean, if it wasn't for them, you know, we'd still be chasing this guy."

Obama decided this week not to release photos of bin Laden himself, saying it would be distasteful and wouldn't satisfy conspiracy theorists. Still, U.S. Secretary of State Hillary Clinton said Thursday in Rome that the al Qaeda leader's killing "sent an unmistakable message about the strength of the resolve of the international community to stand against extremism and those who perpetuate it."

But, she added, "the battle to stop al Qaeda and its affiliates does not end with one death."

Notably, the U.S. continues to devote extensive intelligence and law enforcement resources at home and abroad to rooting out terrorists. And the war continues in Afghanistan, where bin Laden was once hosted and now has 130,000 U.S. and allied troops still battling his followers and his Taliban allies.

Meanwhile, authorities are picking up the pieces from the raid -- not just evidence collected at the compound, but also trying to address fresh wounds and questions pertaining to the relationship between the United States and Pakistan.

Pakistan reacts angrily to tone of U.S. questions

U.S. authorities decided to not to alert their counterparts in the southwest Asian nation prior to the operation fearing the word will leak. And this week, CIA Director Leon Panetta told U.S. lawmakers this week that Pakistani officials were either "involved or incompetent" in bin Laden's case, according to two sources in a closed door briefing.

Pakistan backed the Islamic fundamentalist Taliban's rule over most of Afghanistan before 9/11. Even before Panetta's comments, U.S. officials had warned that some elements of Pakistan's powerful Inter-Services Intelligence agency remain supportive of extremists, even as the country battles its own Taliban insurgency.

But Pakistani Foreign Secretary Salman Bashir said Thursday he felt it is a "false charge" to assert that Pakistani authorities purposefully did not go after bin Laden and "are in cahoots with al Qaeda." He claimed that his country's intelligence agency alerted those in the United States about the presence of al Qaeda operatives in Abbottabad as early as 2004.

Yet he downplayed a potential rift with the United States over the raid, insisting that there has been an "excellent exchange of views" in recent days and that U.S.-Pakistani relations are "moving in the right direction."

At the headquarters of Pakistan's military on Thursday, armed forces chiefs issued a statement admitting that there had been "shortcomings in developing intelligence on the presence of Osama bin Laden in Pakistan." The statement said an investigation will be launched "into the circumstances that led to this situation," but the service chiefs defended the intelligence service's efforts in attacking al Qaeda leaders.

The army chief of staff, Gen. Ashfaq Parvez Kayani, also "made it very clear that any similar action, violating the sovereignty of Pakistan, will warrant a review on the level of military/intelligence cooperation with the United States," the statement said.

Pakistan has ordered U.S. military personnel on its territory drawn down to the "minimum essential" level in the wake of the assault that killed bin Laden, the statement said.

During a Senate Foreign Relations committee hearing Thursday, legislators on both sides of the aisle said a new approach to Pakistan was now needed. Sen. Bob Corker, a Tennessee Republican, said that Pakistan's government is "very irrational."

"How could bin Laden have gone undetected living next door to Pakistan's equivalent of West Point?" said Sen. John Kerry, a Massachusetts Democrat and the committee's chair.

But House Speaker John Boehner, R-Ohio, said that U.S. ties with Pakistan should be further strengthened, if anything. He said, "It's not a time to back away from Pakistan. It's time for more engagement, not less."

Clinton acknowledged the U.S.-Pakistan relationship is "not always an easy" one, but "it is a productive one for both of our countries."

"We are going to continue to cooperate between our governments, our militaries, our law enforcement agencies -- but most importantly between the American and Pakistani people, where we have made a commitment to helping them meet their needs and trying to establish a firmer foundation for their democracy," she said.

CNN's Jeanne Meserve, Samson Desta, Barbara Starr and Elise Labott contributed to this report.