Jonathan had been scheduled to meet some parents of the victims, as well as five girls who escaped captivity hours after the attack in the remote town of Chibok in the northeast.
But a statement from the presidency accused the activists, who started the Bring Back Our Girls campaign, of using the plight of the hostages "to play politics".
“Unfortunately, political forces within the Nigerian chapter of Bring Back Our Girls have decided to take this opportunity to play politics with the situation and the grief of the parents and the girls. They should be ashamed of their actions," the statement read.
"Those who would manipulate the victims of terrorism for their own benefit, are engaging in a similar kind of evil: psychological terrorism."
Some of the president's allies have claimed that the group is working with Jonathan's political opponents and exploiting the kidnapping to embarrass the government.
Jonathan has faced heavy criticism for his handling of the hostage crisis, which many say has lacked both compassion and urgency.
He is not known to have met with any of the girls' families.
"Despite the shameful and disgusting games being played by the Nigerian chapter of Bring Back Our Girls, as a father of girls, I stand ready to meet with the parents of our abducted children," Jonathan said in the statement.
But campaign leader Hadiza Bala Usman told AFP that activists had simply asked to reschedule the meeting so that more parents could attend.
They "requested that the meeting with the president be shifted untill next week to allow for a larger representation", she said.
The meet was hastily organised following talks between Jonathan and Pakistani education rights activist Malala Yousafzai, who urged the president to comfort victims of the mass kidnapping.
Malala, who survived a Taliban assassination attempt in 2012 and has become a champion for access to schooling, was in Abuja on her 17th birthday to mark three months since the Islamist rebels abducted more than 276 girls from a secondary school in Chibok.
At least 219 of the girls taken are still missing.
The Bring Back Our Girls campaign has drawn support from some of the world's most prominent personalities, including US First Lady Michelle Obama and actress Angelina Jolie.
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