Washington (AFP) - One policeman was shot dead and three others shot and wounded in four US cities on Sunday, coinciding with an epidemic of racially-tinged gun violence involving law enforcement.

Police were shot in San Antonio, Texas, Sanibel, Florida, and in the Missouri cities of St. Louis and Gladstone, local police departments said.

There was no known connection between the shootings.

In San Antonio, authorities were hunting for a suspect who fatally shot 20-year service veteran Detective Benjamin Marconi twice in the head after being pulled over in traffic in front of police department headquarters.

Police, who are receiving support from federal and state law enforcement, offered a $10,000 reward for information leading to an arrest in the case, describing the unnamed suspect as a black male wearing a hoodie and baggie pants.

A police officer in Sanibel, on the picturesque island of the same name off the Florida coast, was shot and wounded during a "routine" traffic stop, officials said.

The suspect, who has been arrested, drove by and shot the officer after he had stopped another driver, Sanibel Police Chief Bill Tomlinson was quoted as saying.

In St. Louis, a suspect shot a police sergeant through his rolled up window as he sat in a marked police car in slow traffic.

"It was not a traffic stop. The officer was not trying to detain that person. That individual pulled up next to the officer and started shooting at him," Police Chief Sam Dotson told reporters.

Dotson said the suspect, a black man believed to have been responsible for a "series of crimes" in recent days in the area, including robberies and possibly a carjacking and a homicide, was later shot dead by police after he exchanged fire with other officers.

In western Missouri, another police officer was shot in Gladstone but was expected to live, the Kansas City Fraternal Order of Police said on Twitter. The condition of the suspect was unknown.

Sunday's shootings occurred less than five months after a gunman killed five police officers in Dallas, Texas who were monitoring a protest against high-profile police shootings of black men.

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Just 10 days after the Dallas attack, a man ambushed and killed three law enforcement officers and wounded as many others in Baton Rouge, Louisiana.

And two officers from the Des Moines, Iowa area were shot and killed early this month in a pair of similar attacks while they sat in their patrol cars.