By Farid Ahmed, Catherine E. Shoichet and Steve Almasy

DHAKA, Bangladesh (CNN) -- After hours of quiet at a cafe in the Bagladesh capital where terrorists were holding hostages, a fresh round of heavy gunfire punctured the air Saturday morning, witnesses told CNN.

Media have reported that police stormed the restaurant, Holey Artisan Bakery, in Dhaka.

Armed terrorists may have as many as 20 hostages at the cafe in a diplomatic zone.

The hostage crisis followed a Friday night gunbattle with police that left at least two senior officers dead and 40 people injured.

ISIS claimed responsibility for the terror attack, according to Amaq, an ISIS media branch, but some U.S. officials cast doubt on the claim.

As police exchanged fire with the gunmen, the attackers threw explosives at officers, a source at the scene said.

Here's the latest:

• On Friday evening, gunmen attacked the Holey Artisan Bakery, a cafe popular with expats. They took the people inside hostage, cafe worker Sumon Reza told CNN. Reza said he managed to escape as six to eight gunmen entered. About 20 people, some of them foreigners, were in the restaurant.

• A police officer in charge of a nearby station was shot dead, Maruf Hasan of Dhaka Metropolitan Police said. A second officer died from gunshot wounds, Detective Police Deputy Commissioner Sheikh Nazmul Alam told CNN.

• Alam said 40 people were wounded, some by gunshots and others by shrapnel from explosive devices.

• Ataur Rahman, who was in his office about 200 meters from the restaurant, told CNN he went to the street as he heard a series of gunshots. "I thought it might be an attack somewhere nearby by local thugs." He said people were racing for cover, saying gunmen were shouting "Allahu Akbar."

• "We are trying to resolve this issue peacefully," Benzir Ahmed, the director general of the Rapid Action Battalion of Bangladesh Police, told reporters.

• The Islamic State (ISIS) has claimed a number of past attacks in Bangladesh through its media affiliates, but the government has consistently denied any ISIS presence in the country. Other attacks have been claimed by local Islamist groups.

• Though there was the reported ISIS claim of responsibility, the U.S. State Department said that cannot yet be confirmed. Spokesman John Kirby said the State Department is assessing information.

• A U.S. official familiar with intelligence thinking told CNN's Barbara Starr that based on past operations, it is more likely that al Qaeda in the Indian Subcontinent is conducting this attack -- not ISIS. This is preliminary analysis -- not a conclusion -- based on the best information available. The official says AQIS has demonstrated a more capable presence in Dhaka over the past few months than ISIS, and so far, all of its attacks in Bangladesh have been in Dhaka.

• Witness Sharma Hussain told CNN that her cousin has four friends who are in the restaurant. Hussain said the hostages' relatives have come to the scene but have received no word from their family members. Hussain said she heard the gunshots from her relatives' home, about a five-minute walk from the restaurant.

She said the upscale neighborhood is very secure and residents are surprised an attack happened there. Many of the buildings sit behind walls, have gates in the driveway and security guard booths.

• Police are trying to find out the demands of the gunmen holding customers, an officer said. The gunmen had not made any demands.

• Lori Ann Walsh Imdad, an American teacher living in Dhaka, said she lives one block from the restaurant and she heard gunshots. At first there was a burst of gunfire; after that it was sporadic. There has not been any gunfire since, she said.

• Farzana Azim says she heard explosions outside her home. "We heard the first bomb blast at 8:30 in the evening," Azim said. At first she thought it was the sound of a plane, but a few minutes later another blast echoed through the neighborhood of Gulshan. Within a half hour, the gunshots started, she said.

"I never thought something like this could happen. It is next to a small hospital. This is family-friendly restaurant. Everyone loves to go there," the 49-year-old told CNN.

She said her husband and son had gone outside for the call to prayer and the attack happened shortly after that.

• Hussain said the restaurant is popular among young people, who would have packed the restaurant about the time of attack as they broke their fast for the day.

• Friday's terror attack comes as the holy month of Ramadan, in which Muslims fast from sunrise to sunset, nears its end. Bangladesh is 89% Muslim, according to the CIA Factbook.

• The U.S. Embassy in Dhaka warned of the situation on Twitter, advising people to shelter in place and noting that a hostage situation had been reported. Later, the embassy advised it had accounted for all of the American citizens working under the chief of the mission authority.

• The embassy and many other diplomatic missions are less than 1.5 kilometers (.9 miles) from the cafe.

ISIS or al Qaeda?

CNN terrorism analyst Peter Bergen said he is unaware of an ISIS claim of responsibility that has been proven wrong.

Bergen said he had talked to a counterterrorism official who thought ISIS was to blame for the attack, and that was before the media arm made its announcement. The official said al Qaeda typically doesn't conduct operations with teams this large.

Philip Mudd, a former CIA counterterrorism official and a CNN analyst, agreed with Bergen that ISIS doesn't issue false claims. He said he thinks they were quick to take credit for the attack before al Qaeda could.

"As they compete, they want to get out there in a place like Bangladesh right away before al Qaeda says anything and they say this is us," Mudd said.

ISIS and al Qaeda want to expand their presence around the world, Bergen said. That includes taking homegrown terror groups and making them affiliates.

Country has endured wave of killings

The attack came on the same day a Hindu priest was hacked to death at his temple in Bangladesh's southwestern district of Jhenaidah, police said.

That incident was the latest in a wave of killings across Bangladesh of secular bloggers, academics and religious minorities such as Hindus, Christians, Buddhists and Sufi Muslims -- despite a nationwide government crackdown and the arrest of more than 14,000 people.

The government launched an anti-militant drive across the Muslim-majority nation last month to stamp out the murders, but many of those detained are believed to be ordinary criminals and not Islamic extremists.

Home to almost 150 million Muslims, the country until recently had avoided the kind of radicalism plaguing others parts of the world. But that's changing as the attacks seem designed to silence those to dare to criticize Islam.

One high-profile killing was the murder of Bangladeshi-American writer Avijit Roy in 2014 that occurred right outside Dhaka's annual book fair. In April, a well-known LGBT activist and his friend were murdered.

The trend has sparked debate about the involvement of ISIS.

CNN's Farid Ahmed reported from Dhaka. CNN's Catherine E. Shoichet and Steve Almasy wrote the story in Atlanta. CNN's Joe Sterling and Jareen Imam contributed to this report.

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