UN Security Council Resolution 1970, unanimously adopted this weekend, is important for Libya. But it can and should have an impact around the world.

The arms embargo and asset freeze that the council imposed is significant in symbolic and practical terms. Importantly, the decision to refer Libya to the International Criminal Court sends a signal that the killings will not go unpunished. That has implications going beyond the crimes that may have been committed by Muammar Gaddafi and his associates, important though those are.

This weekend's vote was a historic first. Russia and China, both distrustful of international justice, joined with the once equally wary United States to raise their hands in favour.

Crucially, the referral makes clear that those around the Libyan leader are vulnerable if they remain loyal to his declared policy of killing "cockroaches" and cleansing Libya "house by house". The incentive to desert the murderous ship is thus considerable. The referral is also a warning to anti-Gaddafi forces not to engage in abuses of their own.

In the broader context, the Security Council may finally have begun to haul itself out of the justice-denying rut which it dug itself into in the past six years. In 2005, following pressure from Amnesty International and other human rights organisations, the Security Council referred the crimes against humanity in Darfur to the international court, itself a historic first. In that vote Russia, China and the US abstained.

In the meantime, however, there have been many attempts to challenge the court's authority. Too often, it has seemed that the Darfur referral might remain the exception that proved the bleaker rule.

In recent years, the Security Council has refused to address a number of situations of potential relevance to the International Criminal Court, including the deaths of large number of civilians in – to take just three examples – Gaza, Sri Lanka and Afghanistan.

Following the historic vote at the weekend, the Security Council – too often cynical and shortsighted, in equal measure – must now follow up with a modicum of consistency to its actions in the months and years to come. Resolution 1970 reminds us that justice should not just be an aspiration. It can become a reality, too.

Steve Crawshaw is the international advocacy director of Amnesty International and the co-author of 'Small Acts of Resistance: How Courage, Tenacity and Ingenuity Can Change the World'.