The president said he hoped that "that very soon there will be tremendous progress, which will allow me to get back home".
Speculation over the president's health, and the fact he kept full powers despite his silence, has brought growing unease.
Yar'Adua's refusal to transfer powers to Goodluck Jonathan, the vice-president, prompted a lawsuit from the Nigerian Bar Association, which says the president is violating the constitution.
|Yar'Adua was criticised for not handing powers to his vice-president while ill [AFP]
Felix Onuah, a Nigerian journalist based in the capital, said the protesters wanted to put pressure on the legislators to act.
"They are trying to persuade the National Assembly to invoke a section of the Nigerian constitution to allow the vice-president to take over the affairs of the nation," he told Al Jazeera.
"Their [complaint] mainly is that the president did not hand over power to his vice-before he left for medical treatment abroad."
Andrew Simmons, Al Jazeera's correspondent in Abuja, said: "The protesters say that this has gone on long enough and that they have been fed with misinformation.
"A constitutional crisis is apparently unwinding here ... There is a state of complete limbo."
He said the senate and house of resprentatives in Nigeria were sending delegations to Saudi Arabia to assess the president's health.
'Breach of constitution'
Wole Soyinka, a Nigerian Nobel laureate, said: "The issues are not simply about Yar'Adua being in the country or outside the country. The issues are numerous.
"We challenge him on the continuing corrupt company that we see plotting around and controlling affairs from Aso Rock [the presidential villa]."
Osita Okechukwu, secretary general of a group of opposition parties, said the protesters also called on the National Assembly to brief Nigerians on the president's health, or apply sanctions for a breach of the constitution.
The president's absence also threatens to derail a widely popular amnesty programme that has brought relative peace to the Niger Delta.
Under the measure, thousands of anti-government fighters surrendered their weapons for clemency, a monthly stipend, education and job opportunities.
Former rebel commanders and local activists will decide on Tuesday, after a three-day meeting, whether to continue participating in the programme that has been stalled since Yar'Adua's departure.