KANDAHAR, Afghanistan — Even as they wage a widespread northern offensive, the Taliban have been mounting a multifront attack on two southern Afghan provinces in recent weeks, besieging several districts simultaneously and deeply straining Afghan security forces who in many cases have been surrounded and cut off from resupply, officials say.

Thousands of Afghan soldiers and police officers have been struggling to keep the Taliban out of Lashkar Gah, the capital of Helmand Province. Last week, the fighting came within five miles of the provincial capital. The situation was similar in Uruzgan Province, which borders Helmand to the northwest, according to local officials.

“The Afghan security forces have not made progress in the past seven days of fierce fighting,” said Hajji Mohammad Omar, a member of the Nad Ali district council; Nad Ali district borders the Helmand provincial capital, which appears to be the Taliban’s goal.

Control of Helmand is as much an economic prize as a strategic one because the province accounts for nearly half the opium poppy cultivation in the country, according to United Nations surveys. The province has long been a stronghold for the Taliban, and it was a major focus of the American troop surge several years ago that was aimed at making the district and provincial capitals safer.