RFE/RL's Azerbaijani Service correspondent Ilqar Rasul reports that the large square was packed with people, many adorned with YAP's blue and white colors.
YAP and government officials put the number of demonstrators at 40,000. But this claim could not be verified. Independent observers have said the figure was closer to 10-15,000.
Yesterday, thousands of opposition activists and sympathizers demonstrated on that same Qalaba Square to demand that the outcome of the 6 November vote be annulled and that fresh elections be held.
Official results show that YAP -- which in the outgoing legislature has 75 parliamentary seats -- is set to retain a large, though reduced, majority in the 125-member Milli Meclis, or national assembly.
Addressing reporters at today's rally, YAP Secretary-General Ali Ahmadov denied claims that the polls were falsified in favor of pro-government candidates.
"Azerbaijani society is celebrating victory with us. A new stage in the history of Azerbaijan's democracy and in the development of our society is beginning. Our party won these elections amid tough competition. It has achieved a great victory and we highly value this victory," Ahmadov said.
Earlier today, presidential aide Ali Hasanov called for a truce with the opposition.
Hasanov, who heads the presidential administration's department for political affairs, also called upon anti-government political groupings to "put an end to the election campaign and start thinking about the country's future."
But the opposition today showed no sign it was willing to compromise with authorities.
Addressing a conference of opposition candidates in Baku, the first deputy chairman of the Democratic Party of Azerbaijan (ADP), Sardar Calaloglu, threatened the government with countrywide protests unless it annuls the results of the vote.
ADP is one of the three parties that makes up the Azadliq (Freedom) opposition coalition. The other two parties are Musavat and the reformist wing of the Popular Front of Azerbaijan (AXCP).
Addressing today's conference, AXCP Chairman Ail Kerimli said the opposition should rally as many supporters as possible in anticipation of future protest actions.
"The main problem we're facing now is rallies. We must increase their intensity and bring more and more people. The will of the Azerbaijani people must be expressed on [public] squares," Kerimli said.
Azadliq is planning to hold another rally on 12 November in Baku. It is still not clear whether city authorities will authorize the demonstration.
Kerimli today suggested that protest marches also be held in Azerbaijan's regions.
But Musavat leader Isa Qambar said priority should be given to the planned Baku rally.
"Our next rally should be carefully prepared. We must show the world that we do not accept the results of these elections," Qambar said.
Today's conference ended with Azadliq reiterating a demand that the outcome of the polls be cancelled.
Also represented at the meeting of opposition candidateswere three smaller political groupings: Yeni Siyaset (New Politics), Milli Birlik (National Unity), and the Liberal Party of Azerbaijan, all of which are calling for new elections.
The Organization for Security and Cooperation in Europe and the Council of Europe have criticized the vote, saying it failed to meet international election standards.
The two organizations, however, have not said how the irregularities they documented may have influenced the final outcome.
Election officials have annulled the vote in two of Azerbaijan's 125 constituencies and in 12 polling stations of a third constituency.
As a result of these decisions, the number of parliamentary seats won by YAP has been reduced from 63 to 60, according to a fresh official tally released today.
Yesterday, President Aliyev ordered that two local officials in Baku and Sabirabad be sacked for allegedly interfering in the vote. In addition, the Prosecutor-General's Office has said it has arrested several junior election officials on charges of vote rigging.
Also today, presidential aide Hasanov said election authorities were investigating alleged vote irregularities in 20 constituencies.
But Azadliq, which has officially won eight parliamentary seats, has dismissed these changes as merely "cosmetic."