A second man has been shot by police in the Missouri city where an unarmed black 18-year-old was shot dead last weekend, according to multiple reports.

Police officials told local reporters that the man was shot in Ferguson by a St Louis County officer after pointing a handgun at him soon after 1am on Wednesday, following fresh demonstrations over the death on Saturday of Michael Brown.

The officer was responding to reports of shots being fired and men wearing ski masks carrying shotguns. The man was in critical condition in hospital, a police spokesman told the St Louis Post-Dispatch, Fox 2 and KMOV, and his gun was recovered at the scene.

A woman was separately being treated in hospital after being shot in the head during a drive-by shooting in the city. The incidents followed the peaceful end earlier to a tense standoff between protesters and police, prompting hopes of avoiding a third night of violence.

A raucous convoy of about 250 young demonstrators, marching along a main route into downtown Ferguson, was halted about 30 yards from a wall of police assembled at the entrance to the street where Brown was killed by a still-unidentified officer on Saturday.

Officers in military-style uniforms, some carrying high-powered rifles and wearing balaclavas, formed a line at least two men deep and blocking the entire width of Florrisant Street, the main drag where angry protests over Brown's killing had flared for the previous two nights.

Pitched behind two large armoured trucks, they repeatedly warned the demonstrators through a Tannoy system to "get out of the road or face arrest" – the same warning delivered on Monday night before officers fired teargas, rubber bullets and wooden baton rounds into the crowds.

But for 40 minutes, the protesters defied the threat. Some hung out of car windows, while others raised their arms aloft and repeated what has become their defining slogan: "Hands up, don't shoot." A police helicopter swooped around the dark sky above, shining a bright spotlight on the faces of the almost entirely African American crowd.

"Heavenly father, help us as we continue on this journey of justice," Rasheen Aldridge, a 20-year-old self-appointed leader of the group, told them through a megaphone. "The people behind us, they will do what they will do. Only you can judge us; only you can protect us."

As the police declined to follow through with arrests, furious members of the crowd screamed obscenities at officers and urged them to "shoot those rubber bullets". But after 40 minutes in which it seemed that a repeat of Monday night's clashes would happen at any moment, the protesters abruptly melted away.

Patricia Bynes, a Democratic committeewoman for Ferguson, who was observing the standoff nervously, said she hoped its resolution signalled an end to the violent clashes. "But there is definitely still an antagonism there," said Bynes.

In the early hours of Wednesday it was reported that a small skirmish had resulted in police again using teargas and a young woman being struck in the head with a projectile. Spookwrites, an Instagram user who had previously been covering the protests, posted a photograph of herself wearing a neck brace and showing cuts on her face.

"We have a right to assemble, a right to freedom," said Paul Muhammad. "But here we are facing what looks like a military imposing martial law. It is not acceptable."

The protesters had marched from a church more than a mile away, where earlier in the evening the Rev Al Sharpton, the veteran civil rights leader and TV host, appeared alongside Brown's parents to appeal for calm after two nights in which about 50 people were arrested.

Ferguson police refused on Tuesday to release the name of the officer who shot Brown in sharply disputed circumstances. While police say that Brown assaulted the officer during a struggle, witnesses said he was shot while trying to run away after being grabbed by the officer when he and a friend would not leave the road and walk on the pavement.

For the previous three hours, the officers held their line while being approached by several people who gestured at them or aired complaints. One man, who refused to stop walking, promptly found his chest emblazoned with the red dot of a laser sight from an officer's gun.

Lawanda Wallace, 40, got closer than anyone else to the stone-faced officers and accused them of racism. "It's just the same as 40 years ago," said Wallace. "When white people do it, it's an honest uprising; when black folks do it, it's rioting and looting."

A series of cars, some of whose drivers seemed to be taunting the officers, also approached the police line. One man drove towards them at such speed, and stopped so short of hitting officers, that several people watching gasped and screamed in anticipation of a crash or a shooting to prevent one.

As the man turned his car around and drove away, he poked his head out of his driver-side window and smiled. "I don't know what's up with them," he said of the police.

The Ferguson city police officer who shot Brown has not been named publicly, but has been placed on paid leave while the shooting is investigated by the separate St Louis county police department. The FBI is also looking into whether the incident caused civil rights violations.

In a statement on Tuesday, Barack Obama described Brown's death as "heartbreaking". Noting the FBI investigation, the president appealed for calm. "I know the events of the past few days have prompted strong passions, but as details unfold, I urge everyone in Ferguson, Missouri, and across the country to remember this young man through reflection and understanding. We should comfort each other and talk with one another in a way that heals, not in a way that wounds."

The official response to Brown's death has been rejected as insultingly inadequate by many African American residents of Ferguson, a city of about 21,000 people where 67% of the population is black, yet 94% of the police force – and prominent figures in local government, such as the mayor – are white.