A gunman on a motorbike fired at Yemeni protesters in the coastal town of Hudeida Wednesday, killing one person.
Witnesses say the gunman rode to the edge of the square where protesters are camped and began shooting before speeding off. Several other people were wounded in the attack.
Also Wednesday, a policeman was shot dead during clashes with protesters in the southern city of Aden.
The shootings come a day after security forces fired on anti-government protesters in two other cities, killing six people and wounding 60 others in the capital Sana'a and the southern city of Taiz.
More than 120 people have been killed since near daily-protests began in January calling for an end to the 32-year rule of President Ali Abdullah Saleh.
On Tuesday, the United Nations Security Council failed to agree on a statement calling on the parties in Yemen to "exercise restraint and enter a dialogue." The statement, proposed by Lebanon and Germany, also expressed support for mediation efforts by the Gulf Cooperation Council.
U.N. officials, speaking privately, said Russia and China prevented the council from endorsing the draft statement.
U.S. ambassador to the U.N. Susan Rice said many delegations called for an end to the violence in Yemen and a "swift, credible transition" of power.
Yemen's opposition says nothing short of President Saleh's immediate departure will end the unrest.
Some information for this report was provided by AP, AFP and Reuters.