Several Nigerian newspapers carried a statement asking him to step down that was signed by senior political figures and democracy activists, among others.
But ministers dismissed the statement, saying there was "no basis" for the president to leave office.
Mr Yar'Adua is currently being treated in Saudi Arabia for a heart problem.
In a statement, Information Minister Dora Akunyili said the cabinet had met and had "unanimously resolved" that the president "has not been found incapable of discharging his functions".
She said: "Council wishes to inform all Nigerians that all organs of government are functioning and that government will continue to deliver."
'Leadership vacuum'
BBC Africa analyst Mary Harper says the statement issued by the group of political figures is blunt and to the point.
It says the president's illness "has created a dangerous situation whereby no-one is in charge of the affairs of state".
AFRICAN VIEWPOINT
No journalist worth the description should subscribe to the rumour mill and I try not to, but the Nigerian environment is different
Nigerian journalist Sola Odunfa
Nigeria's great rumour mill
The statement talks about "a vacuum of leadership" whereby ministers are "engaged in infighting" and "routinely flout the orders of the president".
Many of the people who have signed the statement are prominent figures in Nigeria - including Aminu Bello Masari, a former speaker of the House of Representatives, and Ken Nnamani, a former Senate president.
Our correspondent says their words reflect the general mood in the country, where there is real concern that the president's recurring health problems have rendered him frequently unable to do his job.
She says the front pages of Nigeria's newspapers regularly print photographs of a man who is obviously in ill health - his face deeply lined and ashen.
Although he has missed several important events, officials had kept silent on what was wrong with Mr Yar'Adua.
Last week they finally confirmed he was suffering from acute pericarditis - an inflammation of the lining of his heart.
He is also known to have a kidney problem.
source: http://news.bbc.co.uk/1/hi/world/africa/8390750.stm
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