Al-Ibrahimi was speaking on Sunday after meeting the country's US-appointed interim leadership.
A nine-member UN team, which arrived on Saturday, is charged with assessing the feasibility of the rapid elections demanded by the country's Shia Muslim majority.
On Saturday the UN experts met US occupation administrator Paul Bremer.
"The United Nations reconfirms its desire to do everything it can to help the Iraqi people out of its long ordeal and restore independence and sovereignty," said al-Ibrahimi.
Sunday's meeting with the interim Governing Council lasted three hours, and was to be followed up by separate talks with each of its 25 members to sound them out privately on the election issue.
"The United Nations reconfirms its desire to do everything it can to help the Iraqi people out of its long ordeal and restore independence and sovereignty"
UN representative to Iraq
The experts are also set to call on the revered spiritual leader of the country's majority Shia Muslims, Grand Ayat Allah Ali al-Sistani.
The Ayat Allah has spearheaded the call for snap polls, dismissing US plans to handover power to a transitional government by 30 June.
"There is a consensus that elections are needed. The difference is whether they are technically possible," said Intifadh Qanbar, an aide to secular Shia council member Ahmad Chalabi, who is supported by the Pentagon.
But not all 25 members of the Governing Council attended the meeting. At least two, Chalabi and Islamist Shia leader Abd al-Aziz al-Hakim, dispatched representatives.
Al-Hakim met al-Ibrahimi for over an hour on Sunday evening and gave the diplomat what he called a "scientific study", proving that elections can be held.
"In my opinion it is possible and we have submitted a scientific study carried out by experts on the matter," said al-Hakim.
But UN spokesman Ahmad Fawzi said, "We are not here to impose any kind of solution on the Iraqi people (but) to look into the feasibility of elections."
The UN mission would "listen to the Iraqi people, the Governing Council and as many sectors of the Iraqi society as possible, to understand what the Iraqi people want", Fawzi said.
The team is to examine whether it is feasible to organise elections before the end of June, rather than handing self-rule to a transitional assembly selected by provincial caucuses as envisaged by the US-led coalition.
Al-Sistani is the highest Shia
authority in Iraq
According to a 15 November agreement with the Governing Council, the coalition will relinquish power by 30 June to an interim assembly.
Democratic elections for a permanent government are not scheduled until 2005.
For his part, Sunni Islamist politician and current council chairman, Muhsin Abd al-Hamid, confirmed that discussions were still focused on the coalition's deadline for the handover of sovereignty.
"We discussed all the ways for elections to be held for a representative government, while sticking to the June 30 date for the moment," he said.