KABUL, Afghanistan – The governing council of a once-peaceful province in southwestern Afghanistan has fled to Kabul after the Taliban killed one of their members and threatened the others with death. They fear U.S.-led offensives to the east may simply be pushing insurgents into new areas.

The council members from Nimroz province talk of a rising tide of violence as Taliban fighters who have been forced out of neighboring Helmand province, which includes Marjah, shift operations to Nimroz. They say other militants have been crossing into Nimroz from Iran, where they trained at desert camps.

A spokesman for U.S. Marines based in Nimroz insists security has improved in the remote province along the border with Iran and Pakistan.

But Afghan provincial officials say the approximately 2,000 U.S. Marines and 1,000 Afghan soldiers operate primarily in the northeast — 130 miles from the provincial capital, Zaranj — and are unaware of conditions elsewhere in the province.

Nimroz had generally been regarded as peaceful until May 5, when nine suicide bombers disguised as police stormed the provincial council office in Zaranj, about 500 miles southwest of Kabul, killing a woman council member, two police officers and a visitor. All the attackers died. Police said it was the worst attack in Nimroz in two years.

The Taliban claimed responsibility, saying the council was trying to turn Afghans against the militants.

After the assault, the remaining eight council members began receiving death threats.

Council member Shren Azizi said she had just returned home from visiting the family of her murdered colleague when her mobile phone rang.

“Your previous job as a teacher was good for you,” the caller said sternly. “So go back to that if you want to stay alive.”

About five days after the bombing, the council members gathered at their blown-out headquarters. The chairman, Sadiq Chakhansori, decided they’d had enough.

“I put a lock on the door and said, ‘OK, we’re going to Kabul,’ ” Chakhansori said.

Since the roads were too dangerous, the group flew to the western city of Herat and took another plane to Kabul. Only one council member stayed behind — too elderly and ill for the trip.

Provincial Police Chief Gen. Abdul Jabar Pardeli said insurgent activity picked up in Nimroz after each major NATO operation in neighboring provinces. He said he needs more police and troops.

“If they do not help, our security will go from bad to worse,” said Pardeli, who spoke by phone from Nimroz.

Lt. Barry Morris, a spokesman for the Marines in Nimroz, said the U.S. had no evidence of significant militant forces coming into the area from neighboring Farah and Helmand province. He said Marines on patrol in Delaram feel safe enough to shop for carpets.

Council members interviewed this week in Kabul don’t share that view.

Nimroz has long been the most stable part of southern Afghanistan, although it is a major trafficking route for Afghanistan’s huge opium trade. Goods flowing across the Iranian border made the provincial capital relatively prosperous.

But now, Taliban appear to be threatening that border as well. Afghans returning from years as refugees in Iran describe training camps in the Iranian desert used by the Taliban and say weapons trafficking is prevalent, Chakhansori said.

NATO forces recently confirmed that Taliban are training on Iranian soil. In late May, Gen. Stanley McChrystal, the commander of NATO forces in Afghanistan, said that there was “clear evidence” of Taliban training and weapon smuggling in Iran.

The council members are trying to meet with government officials to plead for help. Since arriving in Kabul, they have managed meetings only with the minister of transport and the minister of water and energy, Chakhansori said.

For now, the council members are staying at a government rooming house in Kabul and keeping in touch with their constituents by phone. They say they don’t know what they’ll do if they don’t get any pledges of help.