BEIJING (Reuters) - The United States is looking at ways to increase counter-terrorism cooperation with China, including information exchanges and helping bring stability to places like Iraq, a senior U.S. administration official said on Tuesday.

China was angered last month at a report by the U.S. State Department that said there was a lack of transparency or information from China about incidents it called terrorism, and said counter-terrorism cooperation was limited.

China has tried to encourage Western nations in particular to help in its fight against what it calls Islamist extremists in the violence-prone far western Chinese region of Xinjiang operating as the East Turkestan Islamic Movement (ETIM).

But Western countries have been reluctant to share intelligence with China or otherwise cooperate, saying China has provided little evidence to prove ETIM's existence and citing concern about possible human rights abuses in Xinjiang.

Speaking to reporters on a conference call, a senior U.S. administration official said at the end of a visit to China by U.S. National Security Adviser Susan Rice the threat of terrorism had been discussed in "some detail", along with the importance of Sino-U.S. cooperation in the area.

"Both sides recognize that we, as many others in the international community do, face a threat from international terrorism," the official said, speaking on condition of anonymity.

"We discussed some ways that we could work together to counter that threat. Both in specific areas such as increasing exchanging of information, but also in other ways to contribute to stability in places like Iraq which can also have a positive goal here," he added.

"Certainly, the Chinese did raise their concerns regarding certain organizations like ETIM and both Ambassador Rice and her counterparts had a candid exchange on that as well," he said, without elaborating.

Both countries recognize they and the rest of the international community face a clear danger from the threat of terrorism and will keep looking for ways to increase cooperation in tackling it, he added.

Hundreds of people have been killed in recent years in Xinjiang, home to the Muslim Uighur people, in unrest blamed by Beijing on Islamist militants and separatists, though rights groups say the violence is more a reaction to repressive Chinese policies.

China says ETIM is behind the unrest, though many experts have questioned whether ETIM exists as a cohesive militant group.

China strongly denies abusing anybody's rights in Xinjiang.

(Reporting by Ben Blanchard and Jake Spring; Editing by Robert Birsel)