Kushner -- whose wife Ivanka also plays a key role in advising her father -- accompanied General Joseph Dunford, the chairman of the Joint Chiefs of Staff, on a visit to Baghdad before heading to Arbil, the capital of Iraq's autonomous Kurdish region.
Kushner and Dunford met with officials including Kurdish leader Massud Barzani and the region's prime minister Nechirvan Barzani in Arbil, but journalists were ushered out before the talks got underway.
As in the Trump administration, family ties can translate into senior posts in Iraqi Kurdish government: Nechirvan is Massud's nephew, while the Kurdish chief's sons Masrour and Mansour play leading roles in the region's security forces.
Kushner and White House homeland security adviser Tom Bossert were travelling with Dunford at the general's invitation, according to US Navy Captain Greg Hicks.
The day before, Dunford and Kushner met with Prime Minister Haider al-Abadi and Defence Minister Irfan al-Hayali in Baghdad to discuss the war against the Islamic State jihadist group.
Iraqi forces launched a major operation to retake second city Mosul from IS in October, recapturing its eastern side before setting their sights on its smaller but more densely-populated west.
The grinding battle for west Mosul has taken a heavy toll on civilians, killing and wounding hundreds and pushing more than 200,000 to flee their homes.
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 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.
Valued by Trump for his discretion and loyalty, the baby-faced 36-year-old Kushner 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.
A regular presence in the White House since Trump's election, his 35-year-old daughter and Kushner's wife Ivanka has officially become an assistant to the president amid accusations about possible conflicts of interest involving the couple's business interests, worth hundreds of millions of dollars.