* Talks will resume on April 2
* Conflict has dragged on since 1964 (Updates with FARC news conference)
By Jeff Franks
HAVANA, March 21 (Reuters) - Colombia and the Marxist FARC rebels have made strides toward striking an accord on land reform, but disagreements remain, the two sides said on Thursday at the end of their latest round of peace talks.
Former Vice President Humberto de la Calle said he hoped they could settle the issue quickly when they meet again on April 2, but the rebels said in a news conference they were still adding proposals, which now number 90, for the government to consider.
"There's no step backwards. We're always going forward, advancing slowly if you want to think that way, but also persistently," FARC lead negotiator Ivan Marquez said after reading nine new proposals denouncing such things as free-trade pacts with other countries and the foreign buying of Colombian land.
Tens of thousands of people have died and millions have been displaced during Latin America's longest-running insurgency, a vestige of the Cold War that dates to the FARC's founding in 1964 as a communist agrarian reform movement.
In a joint communique, the government and the FARC said they had made enough progress that they asked the U.N. office in Colombia to start preparation for a public forum on their next agenda item, the FARC's future political participation.
The talks, begun four months ago in Havana, have so far produced no known major advances, which has prompted complaints in Colombia they are moving too slowly.
De la Calle said that considering the complexity of the issues, "the process of construction of an agreement moves ahead normally, although we would like to advance faster."
The two sides are discussing rural development and land reform, the first issues on a five-point agenda, with the aim of addressing the primary cause of the conflict - the South American country's long history of social inequality and land ownership concentrated in the hands of a few.
The FARC, or Revolutionary Armed Forces of Colombia, has proposed giving 20 million hectares (49.4 million acres) of Colombia's land to the poor and establishing a limit on how much property big landowners can have.
While the government has said no land would be taken from private landowners, de la Calle said it was clear there would be no peace without addressing the problems of Colombia's rural poor, including their lack of land for farming.
"Among other actions, profound transformations have to be pushed forward in the countryside, which is where the conflict has principally taken place," he said.
A number of important issues remain to be resolved, including the political and legal status of the rebels, ending the conflict, compensation for war victims, and drug trafficking, which has helped fund the rebels for years.
Colombian President Juan Manuel Santos initiated the talks on the bet that the FARC had been so weakened by a decade-long, U.S.-backed government offensive that it was ready for peace.
The rebels are estimated to have 9,000 troops who have been forced into increasingly remote areas.
They are still capable of launching attacks and did so after the government rejected a two-month long ceasefire the FARC declared at the beginning of the talks on Nov. 19 in Havana.
Cuba and Norway, guarantors to the peace, helped organize the talks after the failure of three previous peace attempts, the last ending a decade ago. The meetings are being held at a Havana convention center.
Chile and Venezuela are also assisting. Santos has said he wants the process ended by November. (Reporting by Jeff Franks, Rosa Tania Valdes and Nelson Acosta; Editing by Kevin Gray and Peter Cooney)