KIEV, Ukraine — A crowded open-air market and nearby homes in Ukraine’s strategically important coastal city of Mariupol came under rocket fire Saturday morning, killing at least 16 people, city authorities said.

Mariupol lies on the Azov Sea and is the major city between mainland Russia and the Russia-annexed Crimean Peninsula. Heavy fighting in the region in the autumn raised fears that Russian-backed separatist forces would try to establish a land link between Russia and Crimea.

Rebel forces have positions within six miles of Mariupol’s eastern outskirts.

The Interior Ministry said rockets struck homes, setting them alight, as well as the market and shops. A Ukrainian military checkpoint on a road leading out of the city toward rebel-held areas was also hit, police said. Mariupol city council said that 74 have been hospitalized.

Rocket strikes on Mariupol come as separatists have declared their intention to mount a multipronged offensive aimed at vastly increasing the territory under their control. That would definitively upend recent European attempts to mediate an end to the fighting.

The city council urged residents not to panic and to ignore rumors that Ukrainian armed forces were planning to withdraw from Mariupol.