October 31, 2004 (Sunday)
- Tabaré Vázquez is elected the next president of Uruguay. (Reuters UK)
- Two days before the 2004 United States presidential elections, President George W. Bush and challenger John Kerry tour the swing states of Ohio, New Hampshire and Florida. (CNN)
- A section of the Berlin Wall is re-erected at the former Checkpoint Charlie as a memorial to the 1,065 people who were killed trying to escape from East Germany. (BBC)
- Three United Nations workers taken hostage in Afghanistan are shown on a video issued by their captors. (BBC)
- Shamil Basayev, the Chechen rebel commander who claimed responsibility for the September 2004 Beslan school hostage crisis, threatens more attacks against Russian civilians. (BBC)
- The 2004 presidential election in Ukraine is held. Preliminary results indicate Viktor Yanukovich in first place with 40% and Viktor Yushchenko in second with 39%. The run-off will be held on November 21. International monitors report "serious irregularities" in the voting. (BBC)
- Darfur conflict: Rwanda begins deploying a contingent of 237 troops to Darfur, Sudan, as part of an African Union mission to bring stability to the troubled region. Sixty-five soldiers have been sent this weekend; the rest will be deployed as the week progresses. Rwanda already had some troops in Darfur. (CNN)
- Conflict in Iraq: 15 Iraqi Shia workers are killed and eight wounded in a rocket attack on a hotel in the predominantly Sunni city of Tikrit. (Reuters)