The war zone of the Democratic Republic of Congo is not a place that is usually associated with hope. The statistics quickly challenge optimism. Since 1998, the country has lost 5.4 million people to conflict, and more than a million people are still displaced in the eastern part of the country. But when I visited eastern Congo last week, there were positive glimmers, in an admittedly still fragile situation. During my time in the region, I met the DRC President Joseph Kabila and Paul Kagame, the President of Rwanda. The two men have traded accusations across Lake Kivu's waters for almost a decade, but speaking to both men I sensed a profound change of mood.

The events of late last year, when the CNDP rebels almost seized the eastern Congolese town of Goma, seem to have shocked both leaders into a tentative attempt at reconciliation. Kagame faced the consternation of donors who accused him of supporting a destabilising rebel group. Kabila almost lost a key government town. This, together with the efforts of UN envoy Olusegun Obasanjo, the former Nigerian president, has clearly shaken the two men into action.

When I met them, both men told me they wanted to find a lasting solution to the problems that have plagued eastern Congo for too long, and both wanted to normalise relations. There was talk of appointing ambassadors and setting up embassies on each other's soil – something that would have been inconceivable just months ago. Of course, there are doubters who will say what these two presidents told me is just lip service. But coming, as I do, with the memory and perspective of the Irish peace talks in mind, I think it would be wrong to underestimate the importance of this nascent relationship between two former foes. It was the good relations between British and Irish government leaders that became the firm foundation of the Irish peace process. This strong relationship anchored resolve when times looked far from auspicious, and ultimately created the path to peace.

I believe the embryonic relationship between Kabila and Kagame is our best chance of ending this bitter and protracted conflict. Now I am back in Europe encouraging European leaders to provide more active support for peace. Congo has fallen off the diplomatic radar, but the situation is still precarious. There is no guarantee further progress will continue without international help. Other governments need to back dialogue between the two countries. They also need to keep the faith by honouring their commitments. The 3,000 extra UN peacekeepers promised last November must be deployed.

Governments in Europe and around the world can also help support the efforts of Rwandan and Congolese women's groups, who see the importance of forging links and building peace at local as well as national level. Women have often been categorised solely as victims of the war in eastern Congo, and there is no doubt they have suffered enormously. I visited the Heal Africa hospital in Goma. The wards were overflowing with women seeking treatment for fistula and other conditions caused by rape – there were literally two women to a bed, with many others waiting outside.

But women are more than just victims. They are agitators for a sustainable peace and agents of change. During my time in the DRC, I met strong female activists who were enthusiastic about working with their sisters in Rwanda to build peace. In Rwanda, I met strong women activists who also want to deepen links across borders.

Both presidents said they wanted to support the efforts of women's organisations working between Rwanda and the DRC to consolidate the peace. Such an exchange would be a way of building confidence between the two countries – and should be supported at the international level too. This is not fanciful optimism: women's group working across the divides in Northern Ireland were instrumental in securing peace there.

With the thawing of relations between Rwanda and the DRC, we have a rare window of opportunity to make a difference to the lives of ordinary people who desperately want to return to their homes and live without the fear of violence. I still hear ringing in my ears the voices of the women in Goma calling for peace and wishing to link with their sisters in Rwanda. I heard the same message from the women I met in Kigali. The glimmer of hope in Congo might not last for long. If we don't act now, this huge country in the heart of Africa could face tragic conflict for yet another decade.

The writer is a former Irish president and honorary president of Oxfam International