Some did get through, however, and footage showed people pushing and shouting next to a door on the floor of the lower house of parliament. On the floor itself, people could be seen shouting, jostling and shoving one another.
Protesters planned to rally again later on Monday.
Police have not disclosed the cause of the journalist's death. Nor has TV Pirveli, the channel he worked for.
Police have detained a new suspect in the violence against journalists, the Interior Ministry said on Monday.
Twenty people had now been detained for violence against media, including five held responsible for physical and verbal abuse against TV Pirveli's camera crew, it said.