The Taliban have seized control of much of rural Afghanistan since foreign forces began the last stage of their withdrawal in early May, but are now focused on capturing provincial capitals, where they are meeting stiffer resistance.
Fighting is raging for Lashkar Gah, the capital of southern Helmand province, with the United Nations saying at least 40 civilians had been killed in the last 24 hours.
General Sami Sadat, commander of the 215 Maiwand Afghan Army Corps, told residents to get out as soon as they could.
"Please leave as soon as possible so that we can start our operation," he said in a message to the city of 200,000 delivered via the media.
"I know it is very difficult for you to leave your houses -- it is hard for us too -- but if you are displaced for a few days please forgive us," he added, AFP reported.
"We are fighting the Taliban wherever they are. We will fight them and... we will not leave a single Taliban alive."
Officials said earlier that the Taliban had seized more than a dozen local radio and TV stations in the city, leaving only one pro-Taliban channel.
"Deepening concern for Afghan civilians... as fighting worsens," the United Nations Assistance Mission for Afghanistan (UNAMA) tweeted.
"UN urges immediate end to fighting in urban areas."
"Fighting was intense this morning," said Sefatullah, director of Sukon radio in the city.
The loss of Lashkar Gah would be a massive strategic and psychological blow for the government, which has pledged to defend cities at all costs after losing much of the rural countryside to the Taliban over the summer.
In Herat, another city under siege, hundreds of residents chanted "Allahu akbar" (God is greatest) from their rooftops after government forces repulsed the latest Taliban assault.
Afghan officials said government forces had managed to push back the insurgents from several areas of that city -- including near the airport, which is vital for resupplies.