* Ceasefire holds in region where 42 died on Tuesday
* Tajik forces offer amnesty to all but four rebel fighters
* Civil casualties reported in Khorog - resident
* State power fragile in mountain region near Afghanistan (Adds OSCE, president comments)
By Roman Kozhevnikov
DUSHANBE, July 26 (Reuters) - Tajik government forces demanded rebel commanders lay down their arms and hand over a former warlord on Thursday, a security source said, as the two sides began a second day of talks after a battle which killed 42 people.
President Imomali Rakhmon called off a military offensive after the fierce fighting on Tuesday in a remote mountain region next to Afghanistan. Troops continued to patrol the streets on Thursday.
The ceasefire in the autonomous Gorno-Badakhshan region followed a campaign to capture former warlord Tolib Ayombekov, a show of strength by a government whose control over parts of the Central Asian state remains fragile 15 years after a civil war.
Twelve soldiers and 30 rebels were killed in the operation to apprehend Ayombekov, who fought against Rakhmon's troops in a 1992-97 civil war before receiving a government job in the peace deal that ended the conflict.
The government has offered amnesty to all rebels except the four fighters, including Ayombekov, it accuses of killing the regional head of the State Committee on National Security, whose murder on Saturday was the trigger for the military offensive.
"We are trying to persuade the fighters to lay down their arms and hand over the four suspects, including Ayombekov," a senior Tajik security source said on condition of anonymity.
"It could take a week or two. That's still better than shooting each other," he said. "Of course, they cannot continue forever. We've suffered heavy losses, but we will suffer more to end this situation if they do not agree to our conditions."
Tajikistan, with a population of 7.5 million, is the poorest of 15 former Soviet republics. Tens of thousands died in its civil war, in which Rakhmon's Moscow-backed troops fought a loosely aligned opposition that included many Islamist fighters.
Former imperial master Russia still has 6,000 troops stationed in Tajikistan, its largest military deployment abroad and a bulwark against the threat of Islamist violence spilling across the Afghan border when NATO pulls its troops out in 2014.
The Organisation for Security and Cooperation in Europe (OSCE), a 56-nation security body currently under Ireland's chairmanship, issued a statement late on Wednesday urging "all parties to exercise restraint".
Khorog, capital of the Gorno-Badakhshan region and the nearest town to the fighting deep in the Pamir mountains, was calm on Thursday, the security source and a local resident said. Most communications were cut off for a third consecutive day.
The local resident, able to communicate via satellite link, said people had returned to work and that shops were open for a second day on Thursday. "We can buy rice, pasta, flour and butter. We are not going hungry," he said.
He said he was aware of at least two civilian deaths, one elderly man and one 18-year-old man caught in crossfire. He said he had attended the funeral of the younger man and that his neighbour had informed him about the elderly man.
The security service source said: "I don't know anything about civilian casualties. I have heard there may be some, as a result of stray bullets."
Gorno-Badakhshan, separated from Afghanistan by the Pyandzh river, is an autonomous region where the authority of the central government is fragile. Most of the 250,000 population sided with the opposition during the civil war.
Ayombekov has denied involvement in the death of Maj.-Gen. Abdullo Nazarov, head of the regional branch of the GKNB, successor to the Soviet-era KGB. The GKNB has said his gang has been involved in smuggling drugs, tobacco and precious stones.
"All criminal groups active in the Pamir should give up their weapons and face justice," the presidential press service quoted Rakhmon as saying on Wednesday at a meeting with the prosecutor-general and government officials. (Writing by Robin Paxton and Dmitry Solovyov; Editing by Myra MacDonald)