A Ukrainian MP says he has not heard from his sister in the city of Mariupol for several days.
Yaroslav Zhelezniak was speaking amid reports of humanitarian corridors opening in several cities, including Kyiv and Mariupol.
The corridors, which will also be opened from the cities of Kharkiv and Sumy, are being set up at the personal request of French President Emmanuel Macron, the Interfax news agency cited Russia's defence ministry as saying.
According to maps published by Russia's RIA news agency and seen by Reuters, the corridor from Kyiv will lead to Belarus, and civilians from Kharkiv will only have a corridor leading to Russia.
Corridors from Mariupol and Sumy will lead both to other Ukrainian cities and to Russia.
Those who want to leave Kyiv will also be able to be airlifted to Russia, the ministry said, adding that it would use drones to monitor the evacuation and "attempts by the Ukrainian side to deceive Russia and the whole civilised world ... are useless this time".
The spokesman for Ukrainian President Volodymyr Zelenskyy said the Russian stance on the corridors was "completely immoral" and that Ukrainians should have the right to evacuate the territory of Ukraine.
Mr Zelenskyy's chief of staff said talks about the limited ceasefire were ongoing.
Deputy Zhelezniak told Newstalk Breakfast it is hard to know exactly what's going on.
"Unfortunately all news from my native town of Mariupol is very bad.
"My sister now today is with her family, small children, in Mariupol.
"And I [don't] have any connection by mobile or internet from here at least last four days.
"Tonight I receive SMS from my cousin, who said that his mother - who is also in Mariupol - find out in one minute [of] internet and SMS that there is a lot of fire around and inside Mariupol.
"There's a lot of shootings, there's no real corridors to evacuate from here."
He says fighter jets were flying over the city "all night".
"There is no electricity, no water, and all food has finished with production.
"So it's a very bad situation".
He says previous attempts to help get people out of those areas has been thwarted by Russia.
"Unfortunately Russian soldiers open fire on people try to evacuate, and it was just impossible to get out from the city".
And he says the situation is the same in many other cities.
"You know the key aims of Russia is to surround Kyiv, our capital, and to get us [to] capitulate.
"But that's why we're highlighting on all levels, on all our messages that we need a no-fly zone on Ukraine.
"It is only one thing which will really save the lives of children, our people, and could help us to stop this bloody war".
Additional reporting: IRN