Iraqi Kurdish forces are a key US partner in the war against IS, which overran large parts of Iraq last year.

Carter's visit to Arbil, the capital of Iraq's autonomous Kurdish region, followed a trip to Baghdad the day before.

There, he met Prime Minister Haider al-Abadi, and the two discussed "improving cooperation between the two countries in the fields of arming and training," a statement from the premier's office said.

Carter and his delegation also met US partners in the international anti-IS coalition.

US aircraft carry out daily air strikes against IS targets, most of them in the Iraqi part of the jihadists' self-proclaimed "caliphate", which also covers regions in Syria.

President Barack Obama said on Monday the US and its allies were hitting IS "harder than ever" and warned the extremists' leaders: "You are next."