(CNN) -- Fighting between Yemen's government and rebel forces erupted Friday as the two sides were working on a peace agreement, a local journalist said.
Fighting in and around the northwestern city of Saada caused the deaths of 13 government soldiers, 19 Houthi rebels and 22 civilians, Houthi rebel sources told Hakim Al-Masmari, the editor-in-chief of the Yemen Post.
Yemen government officials did not confirm the death toll.
Even amid the fighting, the Houthis have presented the Yemeni government with a detailed peace agreement, Yemen's foreign minister told Al-Masmari on Saturday. The government is considering the proposal, he said.
The Houthis, Shiite Muslim rebels, had indicated last week that they were open to a cease-fire and to accepting the government's conditions. But the rebels demanded an end to government military operations first.
The negotiations could put an end to the conflict, which had lasted more than five years.
In August, Yemen laid out cease-fire terms that included removing checkpoints, ending banditry, handing over all military equipment and weapons and releasing civilians and military personnel. Yemen also demanded the rebels stop entering its northern neighbor, Saudi Arabia.
The next month, government officials said Houthi leaders twice rejected the terms.
The conflict is believed to be both separatist, over who will have power in the area, and sectarian, whether Shiite Islam will dominate even though the majority of Yemenis are Sunni.
The rebels are supporters of slain Shiite cleric Hussein al-Houthi.
Humanitarian organization Human Rights Watch has noted allegations of war violations committed by both sides, and fighting has forced 250,000 people to flee their homes, the United Nations High Commissioner for Refugees said.