The Colombian government and the country’s largest rebel group said Wednesday that they had agreed to a cease-fire, clearing a major hurdle in the effort to end one of the world’s longest-running conflicts.

In a joint statement, the two sides said that they had overcome some of the most intractable parts of a peace deal, which they have been negotiating in Havana since 2012.

In addition to a cease-fire, the rebels — known as the Revolutionary Armed Forces of Colombia, or the FARC — agreed to lay down their arms.

The two sides said they would hold a ceremony in Havana on Thursday to mark the cease-fire, attended by Colombia’s president, Juan Manuel Santos, the FARC leader Rodrigo Londoño and other Latin American leaders. Negotiators hope a final peace deal will be reached in the days or weeks to come.