A judge granted them an extra 12 hours to file charges, and they now have until Wednesday evening local time.
Correspondents say police have been put on the defensive by questions over their handling of the case.
All three women are said to be in good health, following their dramatic rescue on Monday evening.
Amanda Berry, who disappeared in 2003 aged 16, escaped with a neighbour's help while her alleged captor was away.
Gina DeJesus, who went missing aged 14 a year later, and Michelle Knight, who vanished in 2002 aged about 19, were also rescued from the property.
A school bus driver, Ariel Castro, and his two brothers - Pedro, 54, and Onil, 50 - have been arrested.
By Jonny DymondBBC News, Cleveland
It is difficult to believe that Seymour Avenue could be home to such a crime: a quiet tree-lined street with houses knocked about and sometimes boarded up, a red-brick church and traffic humming back and forth at either end.
But it is the residents and neighbours who are most surprised. Aurora Marti, 75, has lived across from 2207 Seymour Avenue for 27 years. Ariel Castro used to come and sit on her porch and chat with her. He took her granddaughter out for bike rides at a nearby park.
When the nearby area was being dug up in the search for Amanda Berry's remains, he talked to her about it. All the while he is alleged to have held Amanda and two other women just across the road.
Ariel Castro reportedly fled the neighbourhood after neighbours kicked in the door of his house to help the women escape.
He was arrested at a nearby McDonald's restaurant, according to local media.
It is unclear when Castro's brothers were detained.
The reappearance of the women astounded residents of the neighbourhood in which they had been held, but some have claimed police failed to act on their tip-offs.
Police have confirmed a six-year-old girl, Jocelyn, who was discovered along with the women, is Amanda Berry's daughter.
Police say they are planning to conduct in-depth interviews with the suspects on Wednesday, and charges are expected to be filed by that evening - 48 hours after the men were arrested.
"This is just the tip of the iceberg. This investigation will take a very long time," Cleveland police spokeswoman Jennifer Ciaccia told CNN.
Police are carrying out an inch-by-inch inspection of the house at 2207 Seymour Ave and say they are also searching other properties.
Monday's rescue unfolded with a frenzied call to the emergency services by Ms Berry, now 27.
She escaped with the help of a neighbour who heard her screaming while her alleged captor was out of the house.
Rescuer Charles Ramsey said he had helped kick in a metal door so that Ms Berry could climb outside, with her daughter, and phone police.
In a recording of Monday's emergency call, she says: "I've been kidnapped, and I've been missing for 10 years. And I'm here. I'm free now."
She begged for police to come soon, "before he gets back".
Police then arrived to find the two other abductees.
The women were taken to hospital and reunited with their families.
Medical officials said they appeared to be in good health and were discharged from hospital.
Jocelyn was smiling and eating ice lollies, police said, adding that she had been surreptitiously home-schooled by her mother in the house.
FBI Special Agent Stephen Anthony said on Tuesday: "The nightmare is over. These three young ladies have provided us with the ultimate definition of survival and perseverance. The healing can now begin."
Jaycee Dugard, who was 11 when she was kidnapped in South Lake Tahoe, California, and held captive for 18 years before being rescued in 2009, released a statement saying:  "As simple as it sounds, these women need the opportunity to have the privacy to heal and reconnect.
"I know individuals are strong in spirit and can be resilient in crisis. I wish them the best in their journey."
Startling details about the close connections between the alleged abductors and the families of the abducted have emerged.
Tito DeJesus, an uncle of Georgina (or Gina) DeJesus, played in bands with Ariel Castro and had even visited the house while the women were being held there.
Ariel Castro's son, Anthony, wrote an article about the disappearance of Gina DeJesus for his local newspaper in 2004.
He has been quoted as saying that it was "unspeakable" to discover the suspected perpetrators were in the family.
Neighbours told news organisations they had made multiple calls to police regarding suspicious activity at the house, including sightings of women crying for help.
Another neighbour claimed to have alerted police to the sound of pounding on the doors.
Meanwhile, Ariel Castro was allegedly seen taking a small girl for early-morning walks.
In a statement, Cleveland police insisted they had not been alerted to reports also emerging from neighbours concerning sightings of "naked women and women in chains" at the property.
"Upon researching our call-intake system extensively, only two calls for service from police are shown at that address.
"One call was from the resident, Ariel Castro, reporting a fight in the street. The second call was in relation to an incident regarding Ariel Castro and his duties as a bus driver. Police investigated the possibility that Castro had left a child unattended on a school bus.
"The investigation included an interview with Castro; however, officers did not enter the home. No charges were filed in that incident."
But one resident, Lupe Collins, described as close to relatives of the women, said police had failed the victims.
"Everyone in the neighbourhood did what they had to do. The police didn't do their job."
Cleveland police were heavily criticised in 2009 after officers discovered a home in a poor district in which Anthony Sowell had killed 11 women.
Victims' families allege police did not take neighbours' reported suspicions seriously enough.
Police investigating the abduction of three women for about a decade in Cleveland, Ohio, are due to interview three male suspects.