Colombia's government and the FARC guerrilla group reached agreement Wednesday on the rebels' participation in politics once they end their near 50-year insurgency, the two sides announced.

"We have reached fundamental agreement on the second point of the agenda," they said in a joint statement read out in Havana by a Cuban diplomat, Rodolfo Benitez.

The rebels' return to politics was one of five agenda points under negotiation in year-long peace talks between the government of Juan Manuel Santos and the Revolutionary Armed Forces of Colombia, or FARC.

"This new democratic opening will clear the way for peace to definitely take root, once the conflict ends," said Humberto de la Calle, a former vice president who is the lead government negotiator.

The FARC's top negotiator, Ivan Marquez, also expressed optimism about the prospects for peace.

"The important aspects that we have agreed on so far in terms of political participation give Colombians the possibility of beginning to open the doors to a true democracy," Marquez said.

"Nevertheless, there is a long way to go," he added.

Marquez stressed the need to "respect the right to life, to differences, to a political option, and not stigmatization."

He was referring to a period in the 1980s when members of the FARC demobilized to form the Patriotic Union movement, 3,000 of whose members and leaders were subsequently assassinated.

The sides still must reach agreement on three more issues -- drug trafficking, compensation for victims, and disarmament -- to finalize a comprehensive accord ending Latin America's longest-running insurgency.

They had previously agreed on how to approach land reform and rural development, the first agenda item and the root of the conflict.

"What we have agreed to deepens and strengthens our democracy," said the joint statement.

Norwegian diplomat Dag Mylander, also reading from the joint statement, said the agreement "includes guarantees for the political opposition, measures to promote citizen participation and it contemplates revising the Colombian electoral system after a final peace agreement is signed."

Norway and Cuba are guarantors of the peace talks, which got under way in Havana in November 2012.

Negotiators went into overtime to clinch the agreement on how to reintegrate demobilized rebels, extending talks that were supposed to have ended last Thursday until it was hammered out.

Santos, who is running for re-election in 2014, had urged the FARC to speed up the process.

Shortly before the agreement was announced in Havana, Santos said the day was nearing that Colombia would be "a normal country, a country at peace."

"We have to persevere to put an end to this conflict that has bled us for 50 years," he said.

Santos, however, faces a challenge from the right from his predecessor Alvaro Uribe, who vehemently opposes the peace process.

Uribe has thrown his weight behind Oscar Ivan Zuluaga, who this week began collecting signatures for a presidential run against Santos.

Negotiators will now take a 10-day break before tackling the next agenda item: drug trafficking, which the FARC is alleged to have abetted to finance their operations.

The peace talks are Colombia's fourth attempt to find a negotiated settlement to the conflict.