DONETSK, Ukraine — Ukrainian forces battered the outer suburbs of the rebel stronghold of Luhansk on Sunday, pushing deeper than ever but falling short of retaking the city.

The Ukrainian forces pounded rebel positions in an area called Yuvileiny just west of Luhansk, a rebel spokeswoman and residents said. Some accounts said the forces had established a checkpoint there, though a Ukrainian military spokesman could not confirm that.

Some news reports said that the government forces had retaken the city, which is crucial for the survival of the pro-Russian insurgency here in part because of its proximity to the Russian border. But residents and rebels said Sunday evening that the city was still in rebel hands.

“So far our forces are holding them back,” said a spokeswoman for the self-declared Luhansk People’s Republic who asked not to be identified by name for her safety.