( 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 .
13 soldiers , 19 Houthi rebels , 22 civilians killed , Houthi rebel sources tell newspaper . Comment: Houthis have presented Yemeni government with peace agreement , foreign minister says . Yemen laid out cease-fire terms in August , government says Houthi leaders rejected terms .