The protesters complained of the insensitivity of Jonathan, who did not even meet parents of some of the abducted children when they came to Nigeria's capital earlier this month.
Many schools across the country were closed Thursday to protest the abductions, the government's failure to rescue the girls and the killings of scores of teachers by Islamic extremists in recent years.
Protesting teachers in Abuja also demanded compensation for the families of slain colleagues.
Teacher Precillia Udewaze implored the insurgents to free the girls, saying in a video on the Premium Times newspaper website: "We are begging them, wherever they have kept these girls, please Boko Haram. Boko Haram, please."
In Maiduguri, the northeastern city that is the birthplace of Boko Haram, protesting teachers said they could no longer "tolerate government insensitivity to the plight of the girls and the education sector."
In Abuja, protesters singing, "All we are saying is bring back our girls," to the tune of John Lennon's iconic "Give Peace a Chance," marched to the presidential villa, where they were told Jonathan was not there.
Junior minister Olajumoke Akinjide read a message from the president urging Nigerians to unite and stop criticizing the government.
It was "wrong and most unfair," she said, to suggest the government reacted slowly, adding that the president meets daily with security chiefs on the crisis.
Murmurs of disagreement rose as she declared: "The people of Afghanistan do not blame the government, they blame the terrorists."
Nigerians, she said, should instead be "encouraged to supply useful information to the security services."
That inflamed the crowd, which said residents of Chibok did exactly that, but the military failed to respond to their warnings.
Chibok local government chairman Bana Lawal told The Associated Press that he warned the army of an impending Boko Haram attack two hours before the rebels arrived. Reinforcements never arrived, he said, leaving the road open to the school, where the extremists abducted more than 300 girls and young women. Fifty-three escaped and 276 remain in captivity, according to police.
Residents reported a similar lack of action that could have helped avert at least one of two bomb blasts Tuesday at a bustling marketplace in the central city of Jos. The death toll has risen to at least 130, making them the deadliest bombings yet committed by the Boko Haram extremists, though they have not claimed responsibility.
Market vendors said their suspicions were aroused by a white van parked for hours under a pedestrian bridge, according to Mark Lipdo of the Christian charity Stefanos Foundation. He said they warned soldiers at a nearby checkpoint, but nothing was done. The van contained the first bomb.
Lipdo said there was also no apparent security response to the arrest Saturday of a man wearing a suicide bomb vest who told police that many Boko Haram fighters had orders to plant bombs at churches and public places in Jos.
On Thursday, family and friends continued the search for victims missing in the blasts.
Many may never be identified, Dickson Odeh, a University of Jos student, told The Associated Press after he and other students searched several hospital mortuaries. They were able to identify seven students, some only from ID papers on mutilated bodies.
"It's horrible," Odeh said. "Many bodies are burned beyond recognition."
Inside the Jos University Teaching Hospital, Franklyn Anderson, a 23-year-old student who survived the bombing, cried into her mother's shoulder, "Mommy, mommy that fire was terrible!"
She said she was inside the bustling market buying fried yams when the blast hit.
Lying beside a young woman whose leg was blown off, Anderson, a drama student, thanked God for her survival. "I'll pull through ... because I know God is here for me. He gave me another chance, He gave me another life," she said.
Jonathan and his administration are accused of showing indifference to the plight of the abducted schoolgirls and the tragedies suffered by Nigerians arbitrarily targeted by the extremists, as well as abusive Nigerian security forces. The U.N. Human Rights Commissioner has warned that it is the government's responsibility to protect its citizens.
For years, Jonathan and his military leaders have been saying that victory is at hand, even as the 5-year insurgency has grown ever deadlier. More than 2,000 people have been killed so far this year, compared to an estimated 3,600 in the four previous years.
Boko Haram, which means, "Western education is forbidden," blames Western influences for endemic corruption that keeps most Nigerians in poverty despite the country's oil, mineral and agricultural wealth.
National and international outrage at his government's failure forced Jonathan to accept international help this month to find and rescue the kidnapped girls, mainly technical, intelligence-gathering and surveillance expertise.
Eighty U.S. Air Force personnel have arrived in neighboring Chad and begun their mission manning a Predator drone system to help locate the girls, a U.S. military spokesman said Thursday. Manned U.S. aircraft also are searching from a base in neighboring Niger.
Meanwhile, the U.N. Security Council on Thursday declared Boko Haram a terrorist group and imposed sanctions including an arms embargo and asset freeze at the request of Nigeria, which is serving a two-year term on the council.