Yar'Adua, 58, who returned to Nigeria on February 24 after spending 93 days in Jeddah, where he was being treated for acute pericarditis, has not been seen in public since his arrival.
His return threw the country into confusion and revived concerns of a leadership squabble just two weeks after Jonathan was installed as acting president.
Information Minister Dora Akunyili has advised her colleagues to invoke the relevant section of the constitution which paves the way for his removal from office.
She also accused Yar'Adua's aides of lying about his health.
The protesters, who were blocked from gaining entry into the national assembly, also demanded the implementation of the report of a committee on electoral reforms.
Nigeria has a long history of flawed elections and activists have called for comprehensive electoral reforms ahead of the 2011 general elections.
"We will continue to mobilise Nigerians... to engage in public action, including protests and strike action until these demands are fully implemented in the interest of peace, security and genuine democracy," Bakare told reporters.
Protesters also demanded ministers be fired days after attacks on three villages near the central city of Jos left up to 200 people dead.
Security concerns in rural Nigeria following deadly attacks on three villages outside Jos
Sunday's massacre of predominantly Christian villagers was blamed on Muslim pastoralists.
The security forces faced heavy criticism over their failure to intervene to stop the latest killings when a curfew was meant to be in force.
Although troop reinforcements have been deployed, Jonah Jang, governor of Plateau State, said security lapses had worsened the carnage.
Jang said he had alerted Nigeria's army commander about reports of movement around the area and had been told that troops would be heading there.
"Three hours or so later, I was woken by a call that they [armed gangs] had started burning the village and people were being hacked to death" Jang said.
"I tried to locate the commanders, I couldn't get any of them on the telephone."
Nigerian media reported that the country's national security adviser was sacked on Tuesday. However, it was not clear whether the sacking was linked to the latest sectarian violence.
The chief of police for the Plateau State said on Wednesday that he had asked for extra help to control the level of violence in the area.
"We have requested for reinforcements and have been reassured by the special general that reinforcement is on its way," Ikechukwu Aduba said.
Aduba said that 49 people were to be charged with homicide and conspiracy, and that they had already confessed to being on a revenge mission.
The violence came less than two months after sectarian killings in the region left more than 300 dead, most of them Muslims.
Nigeria is almost evenly split between Muslims in the north and the predominantly Christian south.
The recent bloodshed is limited to central Nigeria, where dozens of ethnic groups vie for control of fertile lands.
The weekend killings add to the tally of thousands who already have perished in Africa's most populous country in the last decade due to religious and political frictions.
Nigerian media also reported that Jonathan Goodluck, the country's acting president, had sacked Sarki Muktar, the national security adviser, on Tuesday.