The mayors of the cities of Sumy and Bilopillia on July 16 urged residents to leave for the weekend.
"If there is an opportunity to leave the city, it's better to use it," Sumy Mayor Oleksandr Lysenko said in a Facebook post.
"I think that today, tomorrow and the day after tomorrow you need to pay a lot of attention to your safety. I ask everyone to take my advice."
He also urged to avoid large gatherings of people and not to ignore air raid alerts.
Bilopillia Mayor Yuriy Zarko also called on residents to move away from the state border.
"It looks like a hard weekend is ahead," he said on Facebook.
"Therefore, I would advise those who have such an opportunity to leave for a couple of days to visit their relatives in the villages, at least 40 km away from the border."