Haaretz published five T-shirt designs including this of a pregnant woman
Israeli officials have described as "tasteless" and inconsistent with army values a popular military pastime of printing violent cartoons on T-shirts.
An investigation in Haaretz daily says the customised shirts are often ordered when troops finish training courses.
One example shows a pregnant Arab women in the cross-hairs of a sniper's sight with the legend "1 shot 2 kills".
Another design shows a child being similarly targeted with the slogan "the smaller they are, the harder it is".
In both images the people being targeted appear to be carrying weapons. A third T-shirt design shows a dead Palestinian baby and the words "Better use Durex" (condoms).
An army statement said the customised clothing was produced outside military auspices, but it pledged to stamp out the use of such imagery by soldiers.
"The examples presented by the Haaretz reporter are not in accordance with IDF values and are simply tasteless," the military statement said.
"This type of humour is unbecoming and should be condemned."
But it admitted that until now there were no military guidelines governing "acceptable civilian clothing" made by its soldiers.
The Israeli military has faced heavy criticism for causing high levels of civilian casualties during its recent Gaza offensive.
The army frequently says it takes care to avoid civilian casualties and blames Palestinian militants for putting them in harm's way.
Many Israeli combat troops deal with Palestinians in the occupied territories
A sociologist quoted by Haaretz, Orna Sasson-Levy of Bar-Ilan University, warned the designs could strengthen, stimulate and legitimise aggression towards Palestinians in the occupied territories.
"There is... increasing callousness," she said. "There is a perception that the Palestinian is not a person, a human being entitled to basic rights and therefore anything may be done to him."
The Haaretz investigation discovered numerous T-shirts depicting violence against Palestinians and appearing to celebrate sexual assault.
Other designs appeared to bear witness to officially prohibited practices, such as "confirming the kill" (shooting lifeless enemies' bodies in the head to ensure they are dead), or deliberately harming religious sites and non-combatants.
The shirts are often printed up to mark the end of basic training and other military courses.
The Tel Aviv clothing firm Adiv, which made many of the shirts, did not comment on the Haaretz report.
It prints up about 500 different patterns for military units each month, Haaretz says, mostly jokes about army life and "a handful reflecting particular aggressiveness, violence and vulgarity".
On Monday, Israel's chief of staff defended his troops against a rising tide of criticism.
"I tell you that this is a moral and ideological army," Lt-Gen Gabi Ashkenazi said in a speech to new recruits.
"I have no doubt that exceptional events will be dealt with. We took every measure possible to reduce harm to the innocent [in Gaza]."
The Haaretz report says the T-shirts tend to be worn strictly in private or in barracks because of adverse civilian reactions and are seen by army psychologists as an expression of bonding within a small, tight-knit unit.
Last week several soldiers were quoted anonymously in the media saying troops had killed Palestinians, including women and children, by hastily opening fire under relaxed rules of engagement in Gaza.