"I am ready to give in to your demands, and if you believe my presence in the (provincial capital) city (Ramadi) does not serve the interests of the region, I am ready to go," said Abd Al-Karim Bargis in an open letter to the province on Saturday.
Bargis defended his period of office in the vast province on the border with Syria, Jordan and Saudi Arabia, saying he had arranged convoys of food and medicine for residents in Falluja when the city was besieged by US troops in April.
On Wednesday, his sons, aged 15 to 30, were snatched by armed men who barged into and torched his family home in Ramadi while he was at work.
Dozens of foreigners have been captured in Iraq in recent months. But little attention has been given to Iraqis being seized.
talks started on Saturday between an Iraqi mediator and a representative of a Kuwaiti firm to try to free seven of the company's employees held captive.
Foreign drivers have flocked to
Iraq for work, despite dangers
The Kuwait and Gulf Link Transport Company sent a representative to Baghdad for talks with Iraqi Shaikh Hisham al-Dulaymi to try to secure the release of three Indians, three Kenyans and an Egyptian seized by a group calling itself the "Black Banners" brigade of the Islamic Secret Army.
The foreigners were seized on 21 July.
On Thursday, the group issued a videotape showing one of the Indian captives, Antaryami, dressed in an orange jumpsuit and with a gun pointed at his head. A voice on the tape threatened to execute one of the drivers unless negotiations got under way.
Armed resistance fighters in Iraq have repeatedly dressed captives in orange suits before killing them.
Al-Dulaymi is the head of a major Iraqi tribal group and
said he had acted as mediator in freeing other captives in Iraq including three Japanese who were released in April and two Russians who were freed the following month.
The captors have said they want the Kuwaiti firm to stop doing business in Iraq, and also want financial compensation for the victims of fighting and air strikes in the small city of Falluja.
India said it was dispatching a special envoy to Iraq to try to secure the release of its nationals.
Kuaum Lata, the wife of captured
Indian truck driver Antaryami
India's junior foreign minister said on Saturday New Delhi's envoy to Oman, who speaks Arabic, was being sent to Baghdad to help secure the release of the men.
The decision came as the captors, who call themselves Holders of the Black Banners, said in a statement it extended the deadline to execute the captives by 24 hours to Saturday 1500 GMT, unless their demands were met.
In related news, a Turkish driver seized in Iraq earlier this month was freed after promising his captors he would not return to the country, CNN-Turk television said on Saturday.
Mehmet Dayar, who was picked up on 17 July after a convoy of trucks came under attack in the northern city of Mosul, was released after 12 days of captivity.
Meanwhile, protests and prayers seeking the release of three Indian nationals continued on Saturday in the north Indian hometown of one of the captives.
Roadblocks leading to driver Antaryami's village of Dehlan, 430km north of New Delhi, were erected by locals, blocking all traffic from entering or leaving.
Authorities in Himachal Pradesh state diverted buses and vehicles along a new route to prevent the traffic jams which were witnessed on Friday when thousands of villagers squatted on the highway leading to Dehlan.
"Roadblocks and protests will continue until the hostages are released," said a villager manning a roadblock.
"Roadblocks and protests will continue until the hostages are released"
a resident of captive Antaryami's native village Dehlan, in India's Himachal Pradesh province
Protesters on Friday blocked roads with burnt tyres, parked vehicles and tree branches while others sat on railway tracks, disrupting train services.
Schools, shops and commercial establishments were closed as thousands shouted anti-government slogans.
Dozens of foreigners have been seized in recent months, most of them truck drivers working for foreign companies delivering supplies to occupation forces or Iraqi companies. At least
eight have been killed - four by beheading.