(Adds details, quotes from memorial prayer, supporters of officer)
By Nick Carey and Edward McAllister
FERGUSON, Mo., Aug 23 (Reuters) - Demonstrators in Ferguson, Missouri, gathered in intense heat on Saturday to pray and mark two weeks since a white police officer shot dead an unarmed black teenager, while supporters of the officer said in a separate rally miles away that the shooting was justified.
No arrests were recorded overnight, marking three consecutive relatively calm nights for the St. Louis suburb following daily unrest since Michael Brown, 18, was shot by Ferguson officer Darren Wilson on Aug. 9.
Authorities had logged dozens of arrests nightly as police clashed with demonstrators in unrest that has focused international attention on often-troubled U.S. race relations.
About 70 people marked the two weeks since Brown's death by praying at a makeshift memorial where he was shot and launching into a rendition of "We Shall Overcome" at the time when the fatal encounter began.
Tracey Stewart-Parks, 52, who works in accounting for a health care firm, carried a sign that read "Mike Brown was someone's son - I walk for their son." She said something similar could have happened to any of her four sons.
"All of them have had to learn the rules of driving black and they're lucky it wasn't them," she said. "This has been a long time coming and I do believe we shall overcome. It's time to rip the Band Aid off this old wound, it's time for change."
The St. Louis County NAACP chapter also plans a march.
About 14 miles (22 km) away in St. Louis, dozens of supporters of the officer gathered at Barney's Sports Pub to raise money for Wilson's family.
"We are here to support you, Officer Wilson, and we've got your back. He has been vilified in the news but his story is coming out," St. Louis resident Mark Rodebaugh said.
A woman who declined to give her name read a statement from rally organizers that said in part, "Our mission is to formally declare that we share the united belief that Officer Wilson's actions on Aug. 9 were warranted and justified and he has our unwavering support."
Little information has been released about the investigation of the shooting. A grand jury of three blacks and nine whites began hearing evidence on Wednesday in a process the county prosecutor has said could run until mid-October.
On Friday night, groups of protesters marched up and down the streets of Ferguson and about 100 demonstrators, marshaled by volunteers from the clergy, held a peaceful protest in a parking lot across from the town's police station.
"Good things happen when people calmly interact, and that is what is happening," Missouri Highway Patrol Captain Ron Johnson told reporters early on Saturday.
The National Guard on Friday began a gradual withdrawal from Ferguson. Johnson said about 20 percent of the force had withdrawn so far.
Authorities remain braced for a possible flare-up of civil disturbances ahead of Brown's funeral on Monday.
St. Louis County Police Chief Jon Belmar told Reuters on Friday night law enforcement plans for the weekend would consist of "trying to prevent what is a criminal element from coming in on top of us."
Police came under sharp criticism, especially in the first days of demonstrations, for arresting dozens of protesters and using heavy-handed tactics and military gear widely seen as provoking more anger and violence by protesters.
In addition to local activists and clergy, a contingent of U.S. civil rights workers and community activists from Georgia, Florida, Detroit and elsewhere have set up shop in Ferguson and say they plan to remain in town for an extended period.
In part they want to work on ways to improve Ferguson, a community of 21,000 that is about 70 percent African American but where almost all the police and local politicians are white.
Civil rights activists say Brown's death followed years of police targeting blacks in the community. The suspension of two area police officers in recent days highlighted the divide.
On Friday, St. Louis County Police Officer Dan Page, a 35-year force veteran, was placed in an administrative position pending an internal investigation after a video surfaced in which he boasted of being "a killer," made disparaging remarks about Muslims and expressed the view that the United States was on the verge of collapse.
Belmar, the county police chief, said the comments by Page, a former U.S. serviceman, were "bizarre" and unacceptable.
Two days earlier, another St. Louis-area policeman, an officer from the town of St. Ann, was suspended indefinitely for pointing a semi-automatic assault rifle at a peaceful demonstrator and yelling obscenities. (Reporting by Nick Carey and Ed McAllister; Writing by David Bailey; Editing by Dan Grebler)