The Mariupol city council says that residents of the occupied city in Donetsk have received messages asking them to attend the "military commissariat."

On its Telegram channel, the council said that the "occupiers" were justifying their move "by the fact that Mariupol will become part of the Russian Federation according to the results of the pseudo-referendum."

The referenda in four occupied regions of Ukraine have been widely criticized by Western governments as illegitimate and a "sham." The last day of voting in today. 

CNN reported on Monday that Ukrainian officials claim Russia is using the so-called secession referendums in occupied portions of the four Ukrainian regions as a pretense to draft Ukrainians into the Russian military.

Ukrainian officials also say that travel for young men out of occupied Ukraine has become much more difficult since Russian President Vladimir Putin announced a partial mobilization. Such travel in Ukraine’s south has been difficult but possible, through humanitarian corridors.

In recent days, however, CNN learned from Ukrainian government sources that travel to Ukrainian-held territory has become much more difficult, and that those official humanitarian corridors have now been effectively closed.

The Mariupol city council, which works from Ukrainian-held territory, said that "Hidden mobilization has been going on in the city for a long time. Mariupol residents received text messages offering residents to work in the so-called state military service. As a result of the fake referendum, this will be done openly."

Mariupol Mayor Vadym Boichenko told a news conference in Kyiv that the already small number of people able to leave the city had further shrunk.

"If a week ago 80-120 people left for Ukrainian held areas per day, in the past day 8 people left Mariupol. This indicates that Mariupol is being closed. […] Those people who remain in Mariupol are in danger. Because they will then forcibly mobilize men," Boichenko said.

He estimated that more than 10,000 men might be called up in Mariupol.

Mick Krever and Victoria Butenko contributed reporting to this post.