Speaking in parliament on Sunday night, Sheikh Hasina said the deadline of 1600 local time (1000 GMT) to surrender had passed and she had "summoned the army and other forces to hunt them".
She said that nearly 700 soldiers of the Bangladesh Rifles were already in detention.
Those in custody are the men who laid down their guns on Thursday after the prime minister promised to send tanks in to crush their revolt. Many others chose to flee.
Sheikh Hasina told parliament she had initiated a search operation codenamed Operation Rebel Hunt for missing guardsmen.
Police say they still do not have the names of more than 1,000 guards they believe were involved.
Sheikh Hasina also said: "I had discussions with [US Assistant Secretary of State] Richard Boucher. I told him I want FBI assistance in the probe. I'd also like Scotland Yard to help us and I have already sought UN support."
In 2004, Scotland Yard detectives helped in the investigation into the bomb attack that injured UK High Commissioner Anwar Choudhury in Sylhet.
About 180 officers were present at the BDR annual meeting when the mutiny broke out - only 33 are known to have survived.
Soldiers fire a salute at the state funeral in Dhaka
The bodies of 70 officers have been discovered so far, many of them mutilated after being shot.
Correspondents say the remains of the other 70 or so have probably either been burned or dumped in fast-flowing sewers. Some of the officers' wives were also killed.
The state funeral on Monday was for about 50 of the officers.
Thousands gathered for prayers at the national parade ground in Dhaka as jets flew overhead in salute.
New President Zillur Rahman and army chief Gen Moeen U Ahmed led the funeral.
Two of the coffins carried the BDR's commander-in-chief, Maj Gen Shakil Ahmed, and his wife Nazneen.
Relatives of those killed had travelled from around the country and there were emotional scenes as buglers played the Last Post.
Police have named six men they accuse of carrying out the mutiny. The six were involved in negotiating the mutineers' surrender.
The government had offered the mutineers an amnesty but once the scale of the massacre became apparent, it said those responsible would be punished.
The army has said that those found guilty of murder will be executed.
Meanwhile, hundreds of guards began returning to their posts on Sunday as ordered.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.