WASHINGTON, Apr. 9 (Reuters) - The U.S. is considering easing advisories against its citizens traveling to China, Deputy Secretary of State Kurt Campbell said on Tuesday, acknowledging concerns that the warnings may have curtailed exchanges between Americans and Chinese people.

Communication channels between Washington and Beijing had largely normalized after months of heightened tensions, Campbell told an event hosted by the non-profit National Committee on U.S.-China Relations.

However, he also warned that Chinese support for Russia's war in Ukraine put stabilizing ties at risk.

The State Department has periodically issued tiered warnings for Americans traveling to China, calling on them to reconsider visits or exercise increased caution due to risks of "arbitrary enforcement of local laws," exit bans and wrongful detentions.

But the two countries' presidents have sought to rebuild people-to-people exchanges as a pillar for managing increasing geopolitical competition between the superpowers.

"I don't want to get ahead of ourselves, but I would just simply say that this is certainly an issue under active consideration," Campbell said when asked if the U.S. would ease the advisories. He said he accepted the premise that they had acted as an inhibition to academic and other exchanges.

China has issued its own travel warnings for the U.S., and criticized what it says is increasing harassment of Chinese nationals by U.S. agents at ports of entry, accusations U.S. officials have rejected.

Despite China's warnings, hundreds of thousands of Chinese students study in the United States compared with only a few hundred Americans in China.

But the State Department's No. 2 diplomat, who has said China helped Moscow "retool" and reconstitute its military after early setbacks in its war in Ukraine, cautioned Beijing in stark terms about its "substantial" support for Russia's war effort.

"We have told China directly if this continues, it will have an impact on the U.S.-China relationship. We will not sit by and say everything's fine," Campbell said.

If Russia gains territory in Ukraine it will alter the balance of power in Europe in ways that are unacceptable to the U.S., Campbell said.

"And we will see this not as just a Russian unique set of activities, but a conjoined set of activities backed by China, but also North Korea," he said.

Campbell also said potentially "hundreds of thousands" of Chinese migrants fleeing weaker economic conditions in China have come to the U.S. in recent months, and that Beijing was aware but did not seem to be taking steps to curtail the flow.

"The numbers that we're seeing are large and, frankly, of gathering concern," Campbell said.

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