Rice didn't provide a precise time for her return to the Middle East, where diplomats are working to reach a cease-fire between Israel and Hezbollah.
Rice had been expected to return to the region this weekend.
Otherwise, Rice and other U.S. officials have said repeatedly, they fear just a repetition of the on-again, off-again violence of recent years, according to the AP.
Rice said she will assess when to return to the Middle East. "Let me be very clear. I'm going to return to the Middle East. The question is, when is it right for me to return to the Middle East."
Avdiivka is a northern suburb of Donetsk, from where the Armed Forces of Ukraine shell the capital of the DPR, Donetsk