Iraqi Prime Minister Haider al-Abadi urged protesters not to demonstrate in Baghdad on Friday because security forces are mobilised in the battle to retake Fallujah.
Protesters, mostly followers of powerful Shia cleric Moqtada al-Sadr, have held demonstrations almost every Friday for weeks to demand a government reshuffle.
Last week they breached the fortified Green Zone, which houses most of the country's top institutions, for the second time in three weeks.
"I call upon our youth to postpone their protest tomorrow, because our security forces are busy fighting in Fallujah," Abadi said, speaking from the command centre for the operation he announced on May 22-23.
Tens of thousands of security forces are deployed in the Fallujah area for an assault aimed at retaking the city from the Islamic State group.
Fallujah, which lies only 50 kilometres (30 miles) west of Baghdad, has been out of government control since January 2014 and is one of only two remaining major Iraqi cities still in IS hands, the other being Mosul.
On May 20, protesters broke into the Green Zone and briefly stormed Abadi's own office, further deepening a political crisis that has been crippling the country for months.
The security forces responded more forcefully than three weeks earlier when Sadr supporters breached the restricted area for the first time and stormed parliament.
Human Rights Watch said in a statement released Thursday its investigations were able to confirm that four people were killed by the security forces during last week's protest.
"Security forces protecting the Green Zone had no legitimate reason to fire on protesters who presented no risk to their lives or others," HRW Middle East director Joe Stork said.
The security forces defending the Green Zone used tear gas canisters and live bullets.
The response angered Sadr and his followers and brought rival militia groups to the brink of confrontation in central Baghdad.
Several military commanders and Baghdad's partners in the US-led coalition had recommended focusing efforts on liberating Mosul first but observers say lauching the Fallujah operation offered the embattled Abadi some political reprieve.