The Bulgarian Defence Ministry said on Wednesday some 20 to 25 soldiers have asked to go home after repeated attacks on their 450-strong light infantry battalion in the holy city.
Ten to 15 more soldiers have requested to be relieved from the unit, which is based in the centre of the tense city, than at the beginning of April, said ministry spokeswoman Rumiana Strugarova.
She would not give exact figures, saying some of the requests were not yet official.
The estimates did not include eight soldiers suffering from combat stress who returned to Sofia on Monday.
"Eight have already returned. Now we have more requests. There are around 20 or 25 in total," she said.
The battalion has sustained repeated machine-gun, rocket-propelled grenade and mortar attacks from Shia forces since their leader Muqtada al-Sadr launched a revolt against the US-led occupation in Iraq earlier this month.
The unit's death toll rose to six last week when a soldier was shot and killed in an ambush, adding fuel to an already intense debate in the Balkan state over the battalion's safety.
On Tuesday, President Georgi Parvanov demanded the troops' base be moved to the outskirts of Karbala, where Polish forces are stationed, after insurgents fired on his entourage when he staged a surprise visit to the unit over the weekend.
Bulgarian officials have repeatedly appealed to the US and Poland, which leads the multi-national division in charge of the area, to provide them with backup.
Bulgarian soldiers voluntarily serve in Iraq. More than 60 of them quit the unit before it left to replace Bulgaria's original peace-keeping force in Karbala in February.