Abutu also ruled that Goodluck Jonathan, the vice-president, could not assume the role of acting president without Yar'Adua making such a written declaration.
The senate, former heads of state, ex-ministers, the bar association and the opposition have all called on Yar'Adua, who is being treated for a heart condition, to formally notify parliament of his absence and allow Jonathan to become acting president.
Abutu ruled two weeks ago that Jonathan could perform executive duties but not be acting president.
Andrew Simmons, Al Jazeera's correspondent in Nigeria, said the decision has helped to clarify the confusing political situation there.
"It has clarified one of the areas - it means the vice-president can act with executive powers of the president but would not be termed formally as the acting-president.
"It might sound like a small point but it is a crucial one, particularly for the ruling party.
"There is an election next year and many people feel there is a lot of power play going on, they feel it is important that the power is not formally handed over as it would allow Goodluck Jonathan to be his own man and make his own changes.
"It also points out that the constitution is slightly ambiguous, but it's not for the judge here to rewrite it. There is still a lot of concern because the president hasn't made it clear what he wants done here."
Only the cabinet, which consists of Yar'Adua's own appointees, has the power to force the president to hand over powers.
It has twice passed resolutions saying it believes he remains fit to govern.
Yar'Adua is receiving treatment for a serious heart condition in Jeddah and his absence has raised fears of a constitutional and political crisis in Africa's most populous country.