The crisis in the relationship between Catalonia and the Spanish state is deteriorating. Apart from Brexit, this is Europe’s greatest challenge since the wars in the Balkans in the 90s.

The campaign for independence by the people of Catalonia from the Spanish state goes back many generations. It has always been peaceful. It has always been non-violent. Or it was until Sunday 1 October. The images of heavily armoured, riot-clad Spanish national police – Guardia Civil – batoning voters young and old and violently seizing ballot boxes, were deeply shocking. The result is that more people took to the streets in support of Catalan independence, and a general strike was held across Catalonia.

The Spanish government has sent several contingents of the army into the region. Monday’s meeting of the Catalan parliament has been ruled illegal by a Spanish court. And there is a threat that the Spanish prime minister, Mariano Rajoy, will invoke Article 155 of the constitution, suspending the Catalan government and parliament, and imposing direct rule.

None of this is likely to deflect the independence movement in Catalonia. On the contrary, as the international experience shows only too often, heavy-handed tactics by the state frequently result in greater opposition and resistance.

Leadership is urgently needed in this crisis: leadership from the Spanish state and leadership from the government of Catalonia – but also critically from the international community, especially the European Union.

We're still trying to implement parts of the Good Friday Agreement 20 years on. But, critically, there is no conflict

Any refusal by the international community to get involved – hiding behind the argument that this is an internal matter for Spain – puts at risk the possibility of reaching a peaceful solution to this very complex situation. This same argument was used in Ireland by successive British governments during the 70s, 80s and early 90s, and it blocked the potential to develop a peace process. Eventually it was set aside and the international community, including the US and EU, made very positive and constructive contributions to the development and success of the Irish peace process.

The imposition of preconditions by the British government also played a negative part in preventing dialogue and mediation. However, collectively we succeeded in overcoming all of these difficulties. Key to that success, and in my view to the unlocking of conflicts and disputes wherever they occur, was a preparedness to engage in an inclusive process of dialogue, without preconditions. That allowed no issue to be excluded from the negotiations, and allowed all issues to be open for discussion.

While no two disputes are the same, the broad principles to address and resolve differences are very similar and can be adapted to suit specific needs. These principles have at their heart the centrality of dialogue and mediation: the process must tackle the causes that lie at the core of the dispute. The process must be inclusive, with all parties treated as equals and mandates respected. All issues must be on the agenda, with nothing agreed until everything is agreed. There can be no preconditions and no vetoes. There can be no attempt to predetermine the outcome or preclude any outcome, and there should be a timeframe. This will provide a dynamic. Participants must stay focused and be prepared to take risks and engage in initiatives to advance the process.

The role of the international community is vital, because international experience shows that the participation and encouragement of international actors in any process of negotiation and mediation can be the difference between success and failure.

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None of this is easy, as our own situation typifies. Twenty years after the Good Friday agreement, we are still trying to implement elements of that and subsequent agreements. But, critically, there is no conflict, and no suggestion that there will be a return to conflict.

Our experience, and that of South Africa, is that no conflict is intractable. Political disputes require political solutions, involving dialogue and mediation. With goodwill, progress can be made, peace can be achieved and politics can take the place of conflict.

Thus far, the Spanish government is refusing to open a dialogue without the Catalans acquiescing to preconditions, including an acceptance that any talk of independence is illegal under Spanish law. In a conversation I had on Thursday evening with the Catalan president, Carles Puigdemont, he assured me that the Catalan government stands ready to talk. I urge the Spanish government to agree to talks and to international mediation. I also call on everyone, but especially the Spanish state, to not use violence in this dispute. The imperative must be to apply peaceful methods to find an agreement.

• Gerry Adams is the president of Sinn Féin