Johnston was snatched at gunpoint from his car as he drove home from work in Gaza City on March 12.
The Palestinian journalists' union has accused the authorities of not doing enough to secure the BBC journalist's release.
"We came to ask those lawmakers about the facts and the truth on the fate of our kidnapped colleague," Shohdy al-Kashef, a member of the local journalists' union, said.
"It's more than a month right now and we are concerned for Alan's life after the statement released two days ago. We came peacefully, but we are being assaulted now."
Last Sunday, a little-known group, Kataeb al-Jihad al-Tawheed (The Brigades of Holy War and Unity), claimed it had killed Johnston, one of the few Western reporters to have both lived and worked in the territory.
The Palestinian government has said that so far there was no proof that the claim is true and the government inisists it is still working to secure his freedom.