Yar'Adua's two main rivals in last April's elections have asked the tribunal to nullify the poll result, alleging widespread fraud.
The tribunal is rounding up its work after six months of painstakingly slow proceedings and Monday's unannounced strike by court workers complaining of poor conditions delayed what was scheduled to be an important hearing.
Lawyers for the two challengers and those representing Yar'Adua and the commission that organised the election were expected to submit their final briefs and the tribunal was supposed to set a date for ruling.
The justice minister, who was present outside locked court premises on Monday morning, told lawyers he would take action to resolve the dispute with court staff and ensure that the tribunal could resume work on Tuesday.
Nigeria is Africa's most populous country and its biggest producer of crude oil. Uncertainty over whether Yar'Adua will keep his job has slowed political and investment decisions.
Official results last April gave Yar'Adua 24.6 million votes compared with 6.6 million to former military ruler Muhammadu Buhari and 2.6 million to then Vice President Atiku Abubakar, the two challengers.
European Union observers reported widespread fraud and intimidation, judging that the elections were "not credible" and "fell far short of basic international standards".
Yar'Adua has acknowledged flaws in the process and pledged to carry out electoral reform, but has also insisted he has a popular mandate.
It would be unprecedented for an electoral tribunal to nullify a presidential election result in Nigeria, and the court would be expected to give an interpretation of the laws governing what happens next.
If the court nullifies the election, experts say Yar'Adua would likely have 21 days to appeal to the Supreme Court during which time he would hold onto his job.
If Yar'Adua loses the appeal or decides against an appeal, experts say he would probably stand down and the Senate President would take over for 90 days during which new elections would be held.
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