The deaths occurred during protests in the town of Sadr in Lahaj province, a hospital official said, speaking on condition of anonymity because he was not authorised to brief the media.
Witnesses said security forces fired tear gas to disperse the protesters, who responded by setting three police vehicles on fire.
Violence also erupted during demonstrations in the Red Sea city of Hodeida, where protesters clashed with government supporters and security forces in a battle that included sticks and rocks.
Thirteen demonstrators were injured, medical officials said.
Yemen has seen large protests in recent weeks demanding the ouster of longtime President Ali Abdullah Saleh, a weak but important US ally in the fight against al-Qaeda. Key tribal allies of Saleh have also joined the protests.
Saleh spoke with the US Homeland Security adviser by telephone on Wednesday and expressed his regret for any misunderstanding caused by his public accusations a day earlier that the US and
Israel are behind the unrest threatening his 32-year rule, the White House said.
During the call with John Brennan, Saleh also reaffirmed his commitment to meaningful political reform. Thousands of people have been demonstrating across the Middle Eastern country in support of
democratic change and Saleh’s ouster.
Brennan responded that comments that seek to lay blame for recent developments in the region are unhelpful.
On Tuesday, Saleh accused President Barack Obama of meddling in the affairs of Arab countries, and asked whether Obama is president of the United States or president of the Arab world.