United Nations Secretary General Ban Ki-moon called in Baghdad Monday for Iraq and the international community to increase assistance for over 2.5 million people displaced by violence in the country.

Ban met Prime Minister Haider al-Abadi as well as President Fuad Masum, Foreign Minister Ibrahim al-Jaafari and parliament speaker Salim al-Juburi during his visit, and also addressed the Iraqi parliament.

Iraqi forces are battling to retake the city of Tikrit, the government's largest military operation yet against the Islamic State (IS) jihadist group, which led an offensive that overran much of the country's Sunni Arab heartland last year.

The conflict has forced a huge number of Iraqis to flee their homes, and Ban said Monday that "additional resources are urgently needed to save lives".

"I call on the government of Iraq and the international community to enhance support to Iraq's displaced and to help alleviate the suffering of all the Iraqi people," Ban said, according to a transcript of his remarks.

He also expressed concerns over "allegations of summary killings, abductions and destruction of property perpetrated by forces and militias fighting alongside Iraqi armed forces".

"Civilians freed from the brutality of Daesh should not have to then fear their liberators," he said, using an Arabic acronym for IS.

Baghdad turned to Shiite militias to shore up its security forces, which were swept aside by the IS-led drive last June.

- Executions, kidnappings -

These forces have played a major role in Iraqi operations that have pushed IS back, but have also been accused of carrying out summary executions and kidnappings of members of Iraq's Sunni Arab minority.

They have also been accused of confiscating or destroying Sunni property.

Iraq must "bring volunteer armed groups fighting in support of the government under government control", said Ban.

Abadi said that "strict orders" had been issued against committing human rights abuses, and pointed to "the absence of reports of this type", his office said.

In reality, abuses are still ongoing, with one fighter telling AFP as recently as Friday that militiamen were torching houses in the town of Awja, where columns of smoke rose from multiple fires and many other homes were charred black from earlier burnings.

Abadi also dismissed reports of earlier violations by pro-government forces as actually being the work of IS, despite the existence of strong evidence that militiamen have killed, looted and destroyed property on multiple occasions.

Ban flew in from Egypt, where he attended an Arab League summit in Sharm el-Sheikh dominated by Saudi-led military action against Yemen's Huthi Shiite rebels.

He was due to travel on to Kuwait for a meeting of international donors on Tuesday called to address a massive funding gap in the response to the conflict in Syria.

- Documented abuses -

The UN office of the commissioner for human rights issued a report in March saying that IS jihadists may have committed war crimes, crimes against humanity and genocide in Iraq.

IS is responsible for a litany of documented abuses, including mass executions, targeting minorities, and abducting women and children.

The report also found that Iraqi forces and allied militias "carried out extrajudicial killings, torture, abductions and forcibly displaced a large number of people, often with impunity".

Human Rights Watch expressed regret that a resolution adopted by the UN Human Rights Council on Friday denounced only atrocities committed by IS.

"With military operations in Tikrit under way, the council missed a crucial opportunity to send a strong signal to Iraq and its allies to take all necessary steps to end abuses by militias and security forces," the watchdog said.

The Iraqi government has received support from Iran and from a US-led coalition of 60 nations, some of which are carrying out air strikes.

The UN's cultural agency has been active in attempting to salvage heritage threatened by IS in both Iraq and Syria.

UNESCO director Irina Bokova visited Baghdad on Saturday to announce several initiatives aimed at boosting protection measures and raising awareness.