The two were involved in an argument before Wednesday's FEC meeting.
Oyo-Ita was being questioned by Kyari and Vice President Yemi Osinbajo just before she was seen angrily gesticulating in a heated argument with Kyari before returning to her seat.
She later returned to have another discussion with Osinbajo before National Security Adviser, Babagana Monguno, also joined the discussion.
The issue died down after Deputy Chief of Staff, Femi Ipaye, asked Oyo-Ita to return to her seat after the scene attracted the attention of everybody in the chambers.
The reason for the conflict is believed to be the leaked memo that Oyo-Ita had allegedly written to President Buhari to warn him about the consequences of recalling former Chairman of the Presidential Task Team on Pension Reforms (PTTPR), Abdulrasheed Maina, to service.
Maina had been recalled and promoted after his dismissal by the Federal Civil Service Commission in 2013 following corruption allegations.
In the letter Oyo-Ita addressed to Kyari's office, she said that her warning was based on the implications Maina's reinstatement would have on the president's anti-corruption war.
The memo cast doubt on the presidency's public stance that it was unaware of Maina's reinstatement as he was promptly fired by the president on October 23 after public condemnation.
President Buhari ordered Maina's 'disengagement' and directed Oyo-Ita to provide a comprehensive report to explain the circumstances of his recall.
Minister of Justice and Attorney General of the Federation, Abubakar Malami and Minister of Interior, Abdulrahman Dambazau, are also allegedly instrumental to the process of Maina's recall.
In 2015, Maina was charged alongside former Head of Service, Steve Oronsaye, Osarenkhoe Afe and Fredrick Hamilton Global Services Limited before a Federal High Court on a 24-count charge bordering on procurement fraud and obtaining by false pretence through the award of fraudulent biometric contracts.
After he was declared wanted over an alleged N2 billion pension fraud, he evaded capture from the EFCC and fled abroad.