"The Taliban have entered the city and are fighting to take over police and NDS (intelligence agency) headquarters, and we fear they will storm the prison to free captured insurgents," Haji Bari Daad, a tribal elder in Tarin Kot, told AFP.
The fighting prompted urgent calls from officials for reinforcements and air support.
"If reinforcements do not arrive the city will collapse into the hands of the Taliban," Karim Khademzai, head of provincial capital in Uruzgan, told AFP.
"The streets are empty and the shops are closed," he said, adding people had nowhere to flee as the city has been surrounded by the insurgents.
The news comes as Taliban are threatening to capture Lashkar Gah in neighboring Helmand province, and northern Kunduz city, which the militants briefly seized last year in a stinging blow to Afghan forces.
Seen previously as a rural militant movement capable only of hit-and-run attacks on cities, the Taliban have demonstrated an alarming new push into urban centers in recent months.
The deteriorating security highlights the struggle of Afghan forces, stretched on multiple fronts, to secure remote provinces such as Uruzgan, where Australian, Dutch and American troops fought for years.
As the Taliban edged closer to Tarin Kot Wednesday, they promised on social media to show leniency towards government forces who surrender unconditionally.
Afghanistan defense ministry spokesman Mohammad Radmanish however rejected what he called the Taliban's "propaganda campaign", saying Wednesday the Taliban would be flushed out from the city's outskirts.