The visit comes as Iraqi forces battle to retake Mosul from IS with support from US-led air strikes that have recently been criticised for causing civilian deaths in the city's west.
Prime Minister Haider al-Abadi's office said the prime minister met with General Joseph Dunford, chairman of the US Joint Chiefs of Staff, as well as Kushner and other officials including White House homeland security adviser Tom Bossert.
They discussed "the battle of Mosul and the international coalition's support for Iraq and the training and arming of Iraqi forces in addition to the [issue] of displaced people," Abadi's office said in a statement.
Iraqi forces have been engaged in a grinding battle for west Mosul since last month, fighting that has pushed more than 200,000 civilians to flee.
Dunford asked Kushner - who has no previous experience in government - and Bossert to accompany him on the trip, Navy Captain Greg Hicks said in an emailed statement.
"General Dunford invited Mr Kushner and Mr Bossert to meet with Iraqi leaders, senior US advisors, and visit with US forces in the field to receive an update on the status of the counter-ISIS campaign in Iraq and Syria," Hicks said, using an acronym for the Islamic State group.
"As well as receiving briefings and updates, Mr Kushner is travelling on behalf of the president to express the president's support and commitment to the government of Iraq and US personnel currently engaged in the campaign," he said.
Civilian casualties
"Mr Bossert is travelling in his role as assistant to the president and will participate in meetings and briefings to reinforce the strong US-Iraqi partnership to defeat ISIS," he added.
Dunford and Kushner were also to meet Iraqi Defence Minister Irfan al-Hayali, ministry spokesman Colonel Laith al-Nuaimi said.
The United States is leading an international coalition that is carrying out air strikes against IS and providing other support to forces fighting the jihadists in both Iraq and Syria.
The operation to retake Mosul, Iraq's second city, began last October, with security forces recapturing its eastern side before setting their sights on the smaller but more densely populated west.
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The coalition has admitted that it "probably" played a role in recent civilian casualties in the city, but has sought to place responsibility for the deaths on IS, saying the jihadists are gathering civilians together and seeking to provoke strikes.
Despite his inexperience, Kushner has become one of the most powerful men in Washington as a trusted adviser to the president with a broad portfolio of responsibilities.
Valued by Trump for his discretion and loyalty, the baby-faced 36-year-old is officially a White House senior adviser with far-reaching influence over domestic and foreign policy.
Among other responsibilities, Trump has tapped Kushner to play a leading role in efforts to secure an Israeli-Palestinian peace deal - an achievement that has eluded experienced policymakers for decades.
Kushner's wife Ivanka, the 35-year-old first daughter, also plays a key role in advising her father.
A regular presence in the White House since Trump's election, she officially became assistant to the president last week amid accusations about possible conflicts of interest involving the couple's business interests, worth hundreds of millions of dollars.
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