Ukraine forces are holding on in Bakhmut

and forced all but a few thousand of the residents to flee.

There are three main arteries that provide lifelines for thousands of Ukrainian soldiers fighting in and around the city. Russian forces have been working to cut them off and are closing in on the last road, according to soldiers and volunteers who regularly used the roads.

The challenge for Ukrainian commanders at the moment is ensuring that if a withdrawal is necessary they execute it at the right time, minimizing losses after holding out for as long as they could. The gravest risk for Ukrainian forces is that they would be encircled, trapped and killed in large numbers.

A more immediate risk is that Russia will make it impossible to resupply the Ukrainian fighters in and around Bakhmut. On Friday, Volodymyr Nazarenko, a deputy commander in Ukraine's national guard, said soldiers defending the critical southern supply line “stand firm.”

If that changes — which it could any day, in either direction — then the calculations of Ukraine's military and political leaders also likely would shift.

The information campaign around the battle also has intensified, with Russia portraying the city as on the verge of capture. Ukraine's deputy defense minister, Hanna Maliar, said in a statement Thursday that Russia was “spreading the narratives that are intended to demoralize the Ukrainian military and society.”

Yevgeny Prigozhin, founder of the Wagner mercenary force that has helped lead Russia's assault on Bakhmut, released a video Friday saying that the Ukrainians had only one road left to escape the city and urged President Volodymyr Zelenskyy to order a withdrawal.

“The pincers are closing,” he said.

It was not the first time that Prigozhin has made bold proclamations, many of which have proved to be false. Still, the precariousness of the Ukrainian grip on Bakhmut has been evident for weeks.

The commander of a Ukrainian drone unit, who goes by the call sign Magyar and has offered frequent updates from inside Bakhmut, said in a video message Thursday that it was “getting harder and harder” to hold the town. On Friday, he posted a video saying his unit had been ordered to withdraw from the city.

DANIEL BEREHULAK — THE NEW YORK TIMES A Ukrainian soldier from the 17th Tank Brigade writes down coordinates to pass on to others as they prepare to fire artillery toward Russian positions near Bakhmut, Ukraine, on Friday. The Russians are pressing their attacks to capture the city.