Hopes of ending the continuing violence were dashed when prime minister-designate Nuri al-Maliki failed to fulfil hopes that he would announce a new government by Wednesday.
Urging quick efforts to quell the raging communal bloodshed, Mr Talabani said "we received a report from the morgue about the deaths in Baghdad that 1,091 people were killed between April 1 and 30.
"We are shocked and angry at the daily reports of unidentified bodies being discovered and of people killed on the basis of their identity," Mr Talabani said in a statement issued by his office.
13 more killed
Just hours later, police discovered 13 more corpses around the capital: five in the southern neighborhood of Al-Dura, two in the western area of Amiriya and six scattered around the downtown region.
Mr Talabani said the overall number of people killed would be "alarming if we include the number of bodies still missing across Iraq.
"I urge all political parties and security forces to quickly move to quell this bleeding from crimes aimed to create doubts between sons of Iraq and disrupt national unity," he added.
Mr Talabani said the current "institutional weakness", a reference to a lack of a new government five months after landmark elections, was "benefiting the terrorists."
Parliament met on Wednesday amid strong expectations that the wait was at an end, but ended up doing little more than hearing the reading of new internal regulations.
The session had been briefly halted when Speaker Mahmud Mashhadani stormed out of the hall after an argument with an MP complaining that her bodyguard had been beaten.
That brought a rebuke from Mithal al-Alusi of the small Iraqi Nation List party. "Iraqi people are dying outside, blood is everywhere and the speaker of the parliament has walked out and ended the session. This is shameful. We only hold one session a week."
No word on cabinet
Yet there was no word from Mr Maliki, who on Tuesday said he was putting the finishing touches on a new cabinet and that he would almost certainly unveil the team on Wednesday. Mr Maliki had said the long-overdue cabinet was "90 percent" ready.
He said candidates to head five key ministries -- interior, defense, oil, finance and foreign affairs -- had also been finalized, adding that interior and defense would be headed by independents who had no links with militias.
The assembly will reconvene on Sunday in only its fifth session since the December elections.
The United States hopes that a government with a broad base will help curb the daily bloodshed and pave the way for the withdrawal of Washington's 132,000 troops from the country.
Raging sectarian violence has left thousands dead across Iraq, mostly Sunni Arabs, in Shiite reprisals after the bombing of a revered Shiite shrine in the northern town of Samarra on February 22.
The bloodshed has torn Iraq at a time when the Sunni-backed insurgency has already left more than 35,000 civilians dead, according to some estimates, since the end of the US-led invasion in April 2003.