(Updates arrests, adds detail)

PANAMA CITY, Feb 15 (Reuters) - Nearly 300 protesters were arrested in Panama on Friday as construction workers clashed with police for the third day running over the shooting death of a fellow worker earlier this week.

A dozen police were injured in Friday's protest, which kept much of the capital paralyzed, with piles of tires burning on busy roads and highways across the city.

Police reported 286 arrests, bringing the number of people detained since Tuesday to around 780, police said.

Protesters also threw stones at riot police in the affluent Paitilla area of the city, home to many of Panama's glass-covered skyscrapers, local television images showed.

It was the latest in a series of clashes since the fatal shooting of a construction worker from the SUNTRACS union during a demonstration on Tuesday over safety conditions.

A construction boom has boosted the country's economy and created a shimmering skyline in Panama City, but union members have been protesting at they say are lax safety standards at the city's many building sites.

SUNTRACS leaders accuse the police of killing Airomi Smith, a union leader, during Tuesday's confrontation as part of an orchestrated campaign. The government says it will investigate.

Speaking to RPC TV on Friday, Panama City Mayor Juan Carlos Navarro called for calm and for the union to return to the negotiating table.

Hundreds of workers marched to the presidential palace late on Thursday to present a series of demands to the government.

They called for new laws governing building-site safety and the resignation of the minister of justice and the head of the national police force. (Reporting by Andrew Beatty)