Details emerged about an alleged plot to attack the city's subways with bombs hidden in bags and possibly baby strollers as local and federal officials jostled over the credibility of the threat.

A Department of Homeland Security memo obtained by The Associated Press said the attack was reportedly scheduled to take place on or around Sunday, with terrorists using timed or remote-controlled explosives hidden in briefcases, suitcases or in or under strollers.

The memo said that the department had received information indicating the attack might be carried out by "a team of terrorist operatives, some of whom may travel or who may be in the New York City area."

Three insurgents had been arrested in Iraq this week, the most recent arrest is confirmed to be on Friday, FOXNews has learned. Officials have told FOX that during the interrogation process the detainees made specific claims about a New York City subway plot. They indicated a specific time frame which was imminent — this Sunday — and method: briefcase bombs.

The memo, issued Wednesday to state and local officials, said that homeland security and FBI agents doubted the credibility of the information, but it provided four pages of advice about averting a possible attack.

One reason New York officials took the information seriously, FOXNews has learned is that one individual passed portions of a lie detector test; although federal law enforcement has continued to call the credibility "doubtful."

In Iraq, individuals also had identified others who they claimed were part of the plot and already inside the United States. A federal law enforcement source said they have been unable to corrobrate major elements of the plot and were not looking for anyone inside the U.S. as of late Friday afternoon because they are not convinced the individuals identified even exist.

When authorities detained a third suspect in the plot, they began to investigate whether a fourth had traveled to New York as part of the scheme, according to a law enforcement official familiar with the case.

The official said the man's trip to New York was described by an informant who had spent time in Afghanistan (search) and proved reliable in past investigations. But the official, who spoke on condition of anonymity because of the ongoing investigation, added that authorities had not confirmed whether the fourth man even exists either.

However one law enforcement source told FOXNews the "plot didn't add up" because the "travel times and routes to the U.S." didn't add up.

Those arrested had received explosives training in Afghanistan, the law enforcement official said Friday. They had planned to travel through Syria to New York, and then meet with operatives to carry out the bombings.

A federal official said one of the suspects arrested in Iraq apparently told interrogators that more than a dozen people were involved in the plot, and that they were of various nationalities, including Afghans, Syrians and Iraqis. The official spoke on condition of anonymity because the investigation is ongoing.

Several of these details related to the suspects were first reported by ABC News.

In Baghdad, spokespeople for the U.S. military and the U.S. Embassy declined to comment about the arrests. Department of Homeland Security spokesman Brian Doyle also said the government has no information that the fourth person possibly connected to the plot "is either here or even exists."

Pentagon spokesman Bryan Whitman said the military obtained intelligence information "during the normal course of our operations." The intelligence led to a military raid in Iraq this week that was conducted by Iraqi security forces, backed by U.S. troops, Whitman said, but added that there was no direct link between the raid and the New York subway threat.

Homeland security officials in Washington downplayed the threat and said it was of "doubtful credibility."

But Mayor Michael Bloomberg (search) and Police Commissioner Ray Kelly vigorously defended their decision to discuss the threat publicly Thursday.

"If I'm going to make a mistake you can rest assured it is on the side of being cautious," Bloomberg said at a news conference Friday.

President Bush, asked Friday if he thought New York officials had overreacted, said: "I think they took the information we gave and made the judgments they thought were necessary."

In New York, thousands of extra police officers flooded the city's subway system, pulling commuters out of rush-hour crowds and rifling through their bags or briefcases.

"Hopefully, God's with me and I'll be OK," Vinnie Stella said while clutching newspapers under his arm as he entered the subway at Penn Station.

An estimated 4.5 million passengers ride the New York subway (search) on an average weekday. The system has more than 468 subway stations. In July, the city began random subway searches in the wake of the train bombings in London.

FOXNews' Catherine Herridge and The Associated Press contributed to this report.