The Rapid Action Battalion or RAB has been surrounding a building in Mirpur where seven including three suspected terrorists have been holed up since Monday night.
The main suspect 'Abdullah' has been termed a dangerous militant by the elite force.
He is being accompanied by two associates, his two wives and children, said RAB Director General Benazir Ahmed on Tuesday, reports a news agency.
They were located on the fourth floor of the six-storey building at Mazar Road.
"We have been able to establish contact with Abdullah over phone. He asked for time when we urged him to surrender. We will give him time because his two children are inside."
"The RAB is ready to storm in. Now everything depends on his decision," the RAB chief told reporters around noon.
Sixty-five residents of the building have been moved to a nearby school building, RAB spokesperson Mufti Mahmud Khan earlier said.
"One among them is Abdullah's sister. He told us to evacuate her along with the others."
Utility supply to the house has been cut off. The residents of the area within Darussalam Thana have been feeling nervous due to the overwhelming presence of law enforcers.
Abdullah has been involved in extremist activities since 2005, RAB chief Benazir told reporters.
A long-time resident of Mazar Road, he has a business for selling pigeons. He also repaired computers and other electronics.
"He said he has 50 Improvised Explosives Devices besides other flammable chemicals inside his flat. We were targeted with gunfire from that location after we cordoned this place off last night. We believe he also has a pistol."
RAB has been surrounding the house since Tuesday midnight following a tip-off received from two terror suspects it earlier detained from a house at Tangail's Elenga.
Several bombs, including some Molotov cocktails, were hurled towards the law enforcers from inside around 1:00am but no-one has been injured in the explosions, he said.