The Pentagon chief was due to meet with Turkish President Recep Tayyip Erdogan and Prime Minister Binali Yildirim, as well as Defence Minister Fikri Isik.
Washington is worried by tensions between Turkey and Iraq as the long-awaited battle to retake Iraq's second city Mosul from IS jihadists enters a decisive phase.
Turkey, which fears the Mosul offensive could boost the influence of anti-Ankara Kurdish militia, says it cannot stay on the sidelines, but Baghdad is firmly against the involvement of Turkish troops.
The US wants Turkey to refrain from military operations in Iraq without the green light from Baghdad, fearing the war of words could jeopardize a fragile pact to keep rival sectarian and ethnic militias out of central Mosul.
Respect for Iraq's sovereignty is an "important principle", Carter told reporters on his plane en route to Turkey.
A senior US defence official said Washington was urging both sides to "tamp down the rhetoric".
"We have been talking behind the scenes to get the Iraqis and the Turks to come to an understanding on how to move forward on Mosul and on Turkish presence in Iraq," the official said on condition of anonymity.
The visit comes as Turkish warplanes carried out deadly strikes on US-backed militias in northern Syria, including Syrian Kurdish fighters.
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The Turkish army said Thursday the raids killed between 160 and 200 militants from the People's Protection Units (YPG), a group considered a terror group by Ankara but an effective force by Washington in the fight against IS.
Carter declined to comment on Turkish strikes on the YPG.
Turkey in August launched an unprecedented operation in northern Syria, sending tanks and troops to back Syrian rebels who have pushed IS from several key areas including Jarabulus and Dabiq.
Rebel fighters captured Dabiq on Sunday in a symbolic setback to the jihadists, as a Sunni prophecy cites the town as the site of an end-of-times battle between Christian forces and Muslims.
Carter said the capture of Dabiq was an "important objective" of the campaign.
"The Turks were carrying the burden of the battle here and did spectacularly well," he said.
"We will be working with them to consolidate that border region, long an objective of theirs and ours, and a very important one in the counter-ISIL campaign."
Tensions between NATO allies Ankara and Washington have grown after the failed July coup in Turkey.
Turkish authorities blamed the putsch on a rogue military group led by US-based Muslim preacher Fethullah Gulen -- charges he denies -- and they have repeatedly demanded his extradition.
Carter is due to visit the United Arab Emirates before a meeting of defence ministers from the international anti-IS coalition in Paris on Tuesday. On Wednesday he will join a NATO ministerial gathering in Brussels.