Cheney is expected on Saturday to reassure Japan, a key US ally in Asia, that it should keep its forces in Iraq despite the kidnappers' threats to murder the hostages unless Japan withdraws its 550 grounds troops. The troops are there to purify water and help in reconstructing schools.
He is also likely to discuss the North Korean nuclear issue and Tokyo's ban on US beef in his first official visit to Japan, which was postponed from a year ago due to the Iraq war.
Cheney's arrival comes just over 24 hours before the expiry of the deadline set by the hostage takers, a group calling themselves the Saraya al-Mujahidiin, for Japan to pull out of Iraq.
The group has warned it will execute aid workers Noriaki Imai, Nahoko Takato and freelance photojournalist Soichiro Koriyama unless its demands are met by 9:00pm Japan time on Sunday (12:00 GMT).
Koizumi, facing his toughest political test, has vowed not to pull the troops out of the southern Iraqi city of Samawa despite appeals from the hostages' families, but some analysts say mishandling the crisis could bring down his government.
This is the second day of protests
The US welcomed Japan's decision to keep its troops in Iraq despite the threats. The US State Department said Washington was working with Tokyo to locate the Japanese hostages.
Before Cheney's visit about 1000 protesters rallied near Koizumi's office urging Japan to pull its troops out of Iraq to save the lives of the three hostages.
Japan was stunned on Thursday after Aljazeera television aired a chilling videotape of the hostages at the feet of heavily armed men.
The three are Imai,18, who had planned to look into the effects of depleted uranium weapons; female aid worker Takato, 34; and Koriyama, 32.
Meanwhile, Japan opened an emergency office at its diplomatic mission in Jordan to coordinate rescue efforts for the hostages, said a Japanese Embassy official on Saturday.
A government task force led by Senior Vice Foreign Minister Ichiro Aisawa, Koizumi's special envoy, arrived early on Saturday in the Jordanian capital Amman, said the embassy's deputy chief of mission Jun Yoshida.
Aisawa was scheduled to meet acting Jordanian Foreign Minister Amjad Majali.
The task force will try to locate the three hostages and assemble the facts of the kidnapping, the Kyodo news agency reported.
Details of the kidnapping remain sketchy and it is unclear where or when they were captured.
Tokyo's controversial troop deployment to Iraq is its first mission since World War Two. Critics said dispatching troops to Iraq violates Japan's pacifist constitution, which bans the use of force to resolve international disputes.
Many Japanese also said they feared the troops could come under attack and suffer casualties, something Japan's military has not experienced since 1945.