Dissident republican gunmen who killed the Belfast-born journalist, 29, should lay down their arms, Father Martin Magill added.
He urged politicians at the North of Ireland’s suspended powersharing Assembly to work together to produce a better life for young people.
Fellow journalists formed a guard of honour as the service for their murdered colleague began in Belfast.
Applause rang out around St Anne’s Cathedral as the coffin was carried in.
The congregation was led by Ms McKee’s partner Sara Canning, her mother Joan, brothers Gary and David and sisters Joan, Nichola and Mary.
n introductory comments, Dean Stephen Forde said: “Lyra was a person who broke down barriers and reached across boundaries.
“This was her hallmark in life, this is her legacy in death.”
He said she was a child of the 1998 Good Friday Agreement which largely ended decades of violence and talked of the hopes for an end to the prejudices of the past and the possibilities of a new future.
President Michael D Higgins, Taoiseach Leo Varadkar and British Prime Minister Theresa May were among those who attended.
Tánaiste and Minister for Foreign Affairs Simon Coveney, Minister for Children and Youth Affairs Katherine Zappone,
British Secretary Karen Bradley and British Labour leader Jeremy Corbyn were also at the service.
Ms McKee was shot as she observed clashes between police and New IRA dissidents on the Creggan estate in Londonderry on 18 April.Her funeral was cross-community and mourners spanned both sides of the border.
Catholic priest Fr Magill said: “I dare to hope that Lyra’s murder on Holy Thursday night can be the doorway to a new beginning. I detect a deep desire for this.”
The service of thanksgiving was held in the Church of Ireland’s St Anne’s Cathedral, a short distance from her north Belfast home.
Fr Magill said: “To those who had any part in her murder, I encourage you to reflect on Lyra McKee, journalist and writer, as a powerful example of ‘The pen is mightier than the sword’.
“I plead with you to take the road of non-violence to achieve your political ends.”
Since the killing many have condemned the culture of violence and coercive control practised by dissidents, the clergyman said.
“We need to send a very different message and so I appeal to those who have information about Lyra’s murder but who haven’t yet come forward to do so now.
“If you want to see an end to these brutal rules, and see a new society built on justice and fairness, on hope and not fear, then you can help build that society by letting the police know what you know.”
He called on political leaders to break the Stormont negotiations impasse.
“I pray that Lyra’s murder may be the catalyst needed for parties to start talking, to reform that which was corrosive in previous assemblies and to begin anew.”Those attending the funeral were asked to wear Harry Potter and Marvel Comics merchandise in tribute to the journalist’s passion for both.
Members of the National Union of Journalists formed the guard of honour.
Her family has paid tribute to a “gentle, innocent soul” whose “desire to bring people together made her totally apolitical”.
The New IRA is an amalgam of armed groups opposed to the peace process and it recently claimed responsibility for parcel bombs sent to London and Glasgow in March.
The PSNI believe the violence in Derry was orchestrated in response to an earlier search by officers aimed at averting imminent trouble associated with the anniversary of the Easter Rising.
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