Coveney and Foster stand 'in solidarity' with Derry residents
Arlene Foster has said she stands in solidarity with those living in Londonderry's Fountain estate.
The DUP leader was speaking to residents affected by violence in the city in recent nights.
Irish Tánaiste (deputy prime minister) Simon Coveney also travelled to Derry to show "solidarity" with those working to "end the rioting and violence".
Police welcomed an "incident free" Friday night in the Bogside and Fountain.
However residents are concerned that trouble could escalate again.
- Derry trouble: PSNI chief warns of children and police safety
- Devices thrown at police treated as 'attempted murder'
- More than 30 petrol bombs thrown at police in Derry
One woman told Mrs Foster she was "terrified" by the violence and added: "We don't want this".
The DUP leader will meet police who have been involved in dealing with disorder later.
Mr Coveney said he was in Derry to "show solidarity with all political, community and youth leaders working to end rioting and violence".
He met residents of the Bogside.
The visits follow six consecutive nights of violence in the city.
"Last night, things were a lot calmer, so I think that's positive news and hopefully we can repeat that in the nights ahead," Mr Coveney said.
"But certainly the previous number of nights were not what we want to see or expect to see anymore, coming from a city like Derry, which has done extraordinary things in recent years towards ensuring the communities can live together peacefully."
'Drag us back'
Mrs Foster said: "I wanted to come today to stand in solidarity with the people - yes in the Fountain - but everybody in the city.
"To say to them 'those law abiding people who live here in the city of Londonderry have to be allowed to live in peace here'."
A number of people have been arrested.
On Saturday, a 22-year-old man was charged with three counts of possessing explosives with intent to endanger life, riotous behaviour, making petrol bombs, possessing petrol bombs in suspicious circumstances and indecent exposure.
A 16-year-old youth who was detained on Friday on suspicion of attempted murder over shots fired at police, has now been released "unconditionally". His solicitor said a complaint would be made to the police ombudsman.
A 17 year old was also arrested on Friday on suspicion of possessing petrol bombs in suspicious circumstances, throwing a petrol bomb and riotous behaviour.
On Saturday, a 50-year-old man admitted disorderly behaviour in the Bogside. The city's magistrates court heard that William McConnell, a painter from Glendale Gardens, was seen approaching debris on Fahan Street and trying to erect a makeshift barricade.
When officers asked him to stop, he refused and became aggressive. He threw a beer can, which hit a police vehicle.
He has been banned from entering the Bogside and the Brandywell and is due to appear before the court again in August.
On Friday PSNI Chief Constable George Hamilton warned it was "only a matter of time" before a police officer or a child is seriously injured over violence.
Police said children as young as eight were involved and accused dissident republicans of being behind the attacks.
The trouble in the city started last Saturday when more than 30 petrol bombs were thrown at police.
The trouble happened at the Fountain estate interface and Nailor's Row in the city's Bogside.
On Tuesday, police said dissident republicans were responsible for automatic gunfire directed at officers.
On Thursday, two viable devices were thrown at officers on Derry's walls, police said.
Police said this was "reckless" and showed "a blatant disregard for life".
'Not in our name'
Hundreds of people gathered on Friday night in the city for a rally against the violence.
They included Sinn Féin president Mary Lou MacDonald, Sinn Féin vice president Michelle O'Neill and SDLP leader Colum Eastwood, along with other party members.
Bishop of Derry Donal McKeown and Jim Roddy, Derry's city centre manager addressed the crowd.
Bishop McKeown said: "You cannot claim to love your country and at the same time cause pain and destruction to the people who live there.
"Nothing can be built with petrol bombs or stones thrown in anger."