Abizaid visited the main U.S. base at Bagram, north of Kabul, and greeted troops in southern Kandahar on Thursday's holiday, military spokesman Maj. Mark McCann said.
The general, who commands all American forces in Iraq as well as Afghanistan, was expected to meet U.S.-backed leader Hamid Karzai (search) at his Kabul palace on Friday.
Other details of Abizaid's schedule were not released.
The United States has around 18,000 troops in Afghanistan, most of them in the south and east of the country where insurgents, including followers of the former Taliban government, are strongest.
A bomb killed two American soldiers patrolling in southern Uruzgan province on Wednesday, though officials say violence has eased since a landmark presidential election last month in which Karzai won a majority.
Abizaid also commands troops posted along Afghanistan's porous border with Pakistan, a mountainous region viewed as a possible hiding place for fugitive Al Qaeda chief Usama bin Laden.