Lyra McKee’s sister has offered to meet the 29-year-old journalists’s killer and support him in “accepting responsibility for your actions”.
Nicola Corner said the unknown gunman’s guilt must be as difficult to live with as her family’s grief.
“It is my hope that you need relief from your guilt,” she said.
Ms McKee was shot dead while observing rioting in Londonderry’s Creggan estate on 18 April. The New IRA said its members were responsible.
Mrs Corner was speaking at a peace rally in the city to mark the end of a three-day walk from Belfast to Derry in memory of Ms McKee.
More than 160 walkers took part in the 70-mile (110km) walk, setting off from Belfast on Saturday and arrived in Derry city centre earlier on Monday evening.
Snow Patrol frontman Gary Lightbody, singer Katie Richardson and Lyra’s Choir, who came together from across Northern Ireland, earlier performed in Guildhall Square.
Lightbody was among 200 people who had joined the walk on the final leg from Drumahoe into Derry.
Mrs Corner told the crowd in Guildhall Square she wanted to speak directly to the person who killed her sister.
“It is my belief that when you went out on the night of the 18 April, you did not intend to turn yourself into a killer,” she said.
“Yet the events as they developed led to that becoming your reality. You are now a killer, now the person who killed Lyra McKee, my baby sister, and you cannot take that back.”
She said she would meet the gunman because “Lyra needs justice and this country demands true peace”.
“I am prepared to be there as you hand yourself in,” added Mrs Corner.
I promise you here and now that I will meet you at any police station anywhere on this island to support you in taking the brave step to hand yourself in and allowing my sister the justice she deserves.
“I know it will not be easy – that’s why I am reaching out to you, because sometimes the right thing is the most difficult.”
She added: “Together we can end this nightmare, because failure is not an option.”
Mrs Corner paid tribute to the community in the Creggan area of Derry where her sister was killed and thanked the 160 people who had given the police information about the night of her murder.
She said her sister’s death could not be in vain. The rally closed with Ms Corner holding up a copy of the 1998 Good Friday peace agreement and urging politicians to end the current impasse at Stormont.
Earlier this month, the detective leading the investigation into Ms McKee’s murder called on the gunman to hand himself in.
Two men have been charged with rioting in the city on the night that Ms McKee was murdered.