Three bombs in quick succession killed at least 10 people and wounded 30 at a wholesale market in the southern district of Dora on Thursday.
Earlier, a car bomb on a main road killed four people and wounded ten. Two more bombs killed two and three people respectively in the eastern, mainly Shia, district of the city.
Al-Maliki has said that Iraq's need for US troops could diminish if the US gave Iraqi security forces sufficient weapons.
"I wish that we could receive strong messages of support from the US so we don't give some boost to the terrorists and make them feel that they might have achieved success."
Al-Maliki criticised Bush for complaining about the manner of Saddam Hussein's execution.
"It seems to me that Bush has given in to domestic pressure"
Nuri al-Maliki, Iraqi prime minister
"It seems to me that Bush has given in to domestic pressure," al-Maliki said of Bush's criticism this week.
He went on to say that his government had "fumbled" the hanging of Saddam, which was marred by Shia officials making sectarian jibes, captured on video.
"Maybe he has lost control of the situation," the prime minister added, saying Bush was normally a strong character.
To add to al-Maliki's worries, former officers and soldiers under Saddam have pledged to escalate attacks after the hanging of their leader.
Sheikh Majeed al-Gaood, who has ties with the former regime's army generals and officers, said the pledge came from Izzat Ibrahim al-Douri, one of the most senior members of the Ba'ath party still at large.
"Izzat urged them to escalate their attacks to attain victory, God willing, against the occupiers and their backers, the traitors."
| Al-Maliki has asked for more US weapons [AFP]|
Al-Gaood said insurgents were ready to offer Washington a "truce", scaling down military operations against US troops if they cracked down on Shia militias.
"The resistance is ready to reduce their attacks against the Americans in return for ending their logistical support to the militias behind death squads and the ethnic cleansing," al-Gaood said.
Al-Douri, with a $10 million reward offered for his capture, was formally chosen to replace Saddam as "leader of the insurgency" by top tribal leaders and Ba'athists, al-Gaood said.
Jalal Talabani, the Iraqi president, said he believed al-Douri was in Yemen.
"It had been said that Izzat al-Douri was in Syria but he is in Yemen. The government has not yet discussed requesting from Yemen to hand him over.
"We have had this information for a while. We have been tracing his movements."