Tearful families of the three pleaded with the government on Friday to rescue their loved ones.
But the premier told a news conference he was not considering withdrawing 550 troops from the southern Iraqi town of Samawa.
"We should not give in to these despicable threats from terrorists," said Koizumi.
About 4000 protesters gathered in a Tokyo park on Friday, waving rainbow-coloured peace flags and holding placards reading, "Government: Don't murder the three people. Pull out the troops."
Aljazeera television aired on Thursday a silent video of the three Japanese, including one woman, held by a previously unknown group called Saraya al-Mujahidiin. The group vowed to "burn them alive" if Japanese troops did not leave Iraq within three days.
The hostages are aid workers Noriaki Imai, 18, Nahoko
Takato, 34, and freelance cameraman Soichiro Koriyama, 32. Their whereabouts are unclear. Imai had left for Iraq on 1 April to study the effects of depleted uranium.
The captors warned they would kill the civilian hostages within three days of airing the tape if Japanese forces did not withdraw from Iraq.
No Japanese soldier has been killed in combat since 1945, and
casualties could undermine support for Koizumi's government whose ruling coalition faces Upper House elections in July.
Captured aid worker Noriaki Imai
is 18 years old
The Iraq deployment is Japan's riskiest military mission since
the second world war, and marks a milestone in the country's shift away from a purely defensive military stance.
Japan's public is sharply divided over the dispatch. Critics
say it violates Japan's pacifist constitution and resent what
they have seen as US pressure to put "boots on the ground" in Iraq.
About 100 protesters gathered near parliament, demanding an
end to the Samawa mission on Friday. Buddhist monks in yellow robes banged drums next to sign saying: "Don't Kill! No More War"
"As we've said in the past, hasn't this Iraq war contributed
to an expansion of terrorism, rather than leading to its
prevention?" Democratic Party leader Naoto Kan told parliament.
Tokyo residents are worried about a possible attack in the
nation's capital, while in Samawa, blasts were reported again on Thursday near the Japanese soldiers' camp.
There were no reports of casualties or damage, but the troops have suspended their reconstruction work outside the camp.
Meanwhile, Japan's government has decided to organise an airlift to evacuate Japanese civilians in Iraq to neighbouring Kuwait, a news report said on Friday.
Seventy journalists, non-government organisation workers and other civilians will be evacuated, reported the Yomiuri Shimbun.
The Foreign Ministry and the military declined to comment on the reports.