ST. MARTINVILLE, Louisiana (CNN) -- A white flag appeared from a
                  second-story window as SWAT team members suited up in full riot gear
                  outside the Louisiana jail where a group of Cuban detainees is holding three
                  hostages and demanding to leave the United States.

                  In the midst of those developments Tuesday night, a school bus and two
                  ambulances were brought to the scene.

                  Authorities wouldn't comment on the significance or whether a
                  breakthrough had been reached.

                  Authorities had said earlier in the day that there had been no progress in
                  negotiations with the Cuban nationals who have held a St. Martin Parish jail
                  warden and two correctional officers as hostages.

                  "We are involved in sensitive negotiations and are trying to bring this to a
                  peaceful resolution," said Mike Gilhooly, a spokesman for the Immigration
                  and Naturalization Service (INS).

                  The INS, FBI and state hostage negotiators were in communication with the
                  hostage-takers, trying to end the standoff.

                  No injuries have been reported in the disturbance, which began Monday
                  evening when an inmate pulled a homemade knife on a guard as several
                  inmates left an exercise area.

                  Another hostage, a deputy sheriff, was released after six hours of
                  negotiations. Other inmates were moved to more secure locations in the jail.

                  Hostage execution threat reported

                   As the talks wound on, state and local authorities were increasingly
                   tight-lipped about the standoff and acknowledged that other Cuban
                  detainees had joined the five original hostage-takers.

                  "We're looking into the possibility that an additional three to four detainees
                  may have joined in with the others," said St. Martin Parish Sheriff
                  Department Capt. Audrey Thibodeaux.

                  A local radio station reported that the inmates had set a 72-hour deadline to
                  be freed before the hostages would be killed -- but Thibodeaux said that
                  was not yet confirmed.

                  Kriss Fortunato, an FBI spokesman, acknowledged, "It's being examined."

                  Hostage-takers demand to leave U.S.

                  The prisoners allowed CNN affiliate KLFY inside the facility Tuesday. The
                  two corrections officers appeared weary, handcuffed to their chairs and their
                  legs shackled. Two men in orange jumpsuits stood nearby, one holding a
                  knife with a 6-inch blade taped to his wrist; in the other hand, he held a
                  walkie talkie.

                  The two hostages did not appear harmed. The warden was held in a
                  separate room.

                  "We want to be released and sent back to our country or any other country.
                  We don't care," said Jonne Ponce, one of the Cubans who telephoned
                  KLFY in nearby Lafayette.

                  Ponce said he has been held for 13 years and was frustrated by the lack of
                  progress in his case with the INS.

                  A caller claiming to be a hostage-taker told CNN's Miami bureau that the
                  hostages were taken because the Cubans were tired of being held against
                  their will -- "It was repression. It was imprisonment for nothing. We have no
                  choice."

                  Asked what their demands are, the caller, who refused to give his name,
                  said, "We want to get out of this country."

                  The five Cuban nationals were being held there on behalf of the INS,
                  Thibodeaux said. She said she did not know why the five were detained.

                  "They're detainees, and we house them," she said.

                  3,500 'excludables' behind bars in U.S.

                  Gilhooly said the INS would not release information about the individual
                  Cuban detainees involved in the hostage situation because of the sensitive
                  nature of the incident.

                  Although officials would not comment on why the Cubans were imprisoned,
                  the lack of diplomatic relations between the United States and Cuba often
                  leaves so-called undeportable detainees -- non-U.S. citizens convicted of
                  crimes in the United States who have served their sentences but who cannot
                  be deported back to their native country -- behind bars for years, their lives
                  in limbo.

                  There are about 3,500 held in the United States, mostly Cubans; their
                  countries refuse to take them back, so they remain in the U.S. prison system.

                  State Department spokesman James Foley acknowledged the sensitivity of
                  the detainees, also known as criminal excludables, at a news conference
                  Tuesday.

                  "The Cuban government has not agreed to accept the return of such
                  individuals," Foley said. "We will continue to work together on this issue. It
                  is a long-standing problem. We haven't found a solution to it yet, but we're
                  going to continue to work the issue," he said.

                  The jail houses 160 inmates in a two-story building in downtown St.
                  Martinville, a town of 7,000 about 115 miles west of New Orleans. Sixty of
                  those inmates are Cuban. Officials described it as a typical intergovernmental
                  arrangement like those with numerous county jails around the nation.

                  The jail is about 50 miles from Oakdale, where a federal deportation center
                  was burned by 1,000 rioting Cuban inmates in 1987. Twenty-eight
                  employees were taken hostage and held for eight days before all were
                  released unharmed.

                     Correspondent Ed Garsten and The Associated Press contributed to this report.