Governments in democratic countries must work to bring the perpetrators of persecution to justice, Lord Alton told a major religious freedom summit in Washington DC this week.
Addressing the Ministerial on Religious Freedom, the cross-bench peer said that action needed to be taken against governments that "ignore their responsibility to defend religious freedom".
He said that Christians were the "most persecuted group in the world" and that the "priority" lay in bringing the perpetrators to justice.
"And look at the consequences when we don't," he said, citing the Armenian Genocide and the Holocaust as two examples of what occurs because of "the world's indifference and unwillingness to insist on justice".
"Genocide begins when we ignore the 'canary in the mine' and when we forget our duty to uphold justice," he said.
"Ignore it and it emboldens perpetrators who believe we are too weak or too disinterested to ever hold them to account."
He said that more legal mechanisms were needed to ensure the necessary legal action could be taken at the international level.
"There is little point collecting evidence if we do nothing about it," he said.
"Demonstrating their belief in the rule of law, like-minded nations, signatories to the Genocide Convention, should establish ad hoc tribunals and legal mechanisms of their own."
Referring to US religious freedom ambassador Sam Brownback's call earlier on in the summit for a grassroots movement to advance religious liberty, he said this required a "new determination to uphold justice".
"The alternative is to allow mass murderers to grow old, unpunished and to believe they can continue their depredations with impunity, never facing their Nuremburg Moment," he said.
Lord Alton condemned China over its treatment of Christians and minority faiths, including forced organ harvesting from prisoners of conscience and the imprisonment of at least a million Uighur Muslims in re-education camps.
"What a disgrace that we sell face reconstruction and other surveillance equipment to a regime that has incarcerated its own people," he said of the UK.
"Little wonder that millions of protesters in Hong Kong, fearful of losing their right to religious freedom and political freedoms have taken to the streets singing as their anthem, Hallelujah to the Lord. I salute the courage of the people of Hong Kong."
He continued: "When you ignore the canary in the mine it leads to the incarceration of Uighurs in China, the unfolding Jihad in Nigeria, the burning alive of Christians in Pakistan, the displacement of Muslim Rohingya and Christian Kachin in Burma – and to genocide. Genocide unchecked; genocide unchallenged; genocide unpunished."
He went on to say that Western aid programmes were "too often religion blind" and needed to be shaped to promote religious freedom as a priority.
"We cannot afford the luxury of silence," he said.
"The Protestant theologian, Dietrich Bonhoeffer, executed by the Nazis famously said, 'Not to speak is to speak, not to act is to act.'
"In contesting the persecution of millions, including 250 million Christians [...] future generations will judge us on how we responded.
"And rightfully so. The test for each of us will now be: how will we speak? How will we act? What are we going to do about it? Now, not later."