Under the accord, the ruling National Congress have 52% of the seats and the former southern rebels 28%.
The BBC's Alfred Taban in Khartoum says some opposition parties have complained that the president's party is unfairly dominating both chambers.
With south Sudan making up a third of the country, they do not dispute the power-sharing allocation given to former rebels, the Sudan People's Liberation Movement (SPLM), he says.
But they say it is not good for democracy for the National Congress to take more than half the seats.
National Congress members were elected speakers of the National Assembly and Council of States.
Not a single day goes by without two, three or four attacks on aid convoys
Unicef's Keith McKenzie
The deputy speakers come from the SPLM, although they did not show up at the opening.
There was concern that the peace deal would be derailed by the death last month of SPLM leader John Garang, one of the main architects of the accord.
But his successor Salva Kiir, now Sudan's first vice-president, says he is committed to Garang's vision.
Our correspondent says a new legislative chamber will be set up in three to four years' time to pave the way for the south to hold a referendum on secession in six years' time.
The civil war pitted the Muslim north against Christians and animists in the south, leaving some 1.5 million people dead.
In his speech, President Bashir, who came to power in an Islamist-backed coup in 1989, reiterated his determination to "find a peaceful solution" to the conflict in the western region of Darfur.
Meanwhile, the United Nations Children's Fund (Unicef) has said attacks on humanitarian aid convoys by bandits in Darfur have become rampant.
"Not a single day goes by without two, three or four attacks on aid convoys," Unicef's representative in Darfur, Keith McKenzie, told a new conference in London.
He said Darfur's 11,000 aid workers were doing an excellent job, but he warned that the rising level of lawlessness was making some agencies consider reducing their presence at a time when the need for their help was growing.
The number of refugees in the region has risen to more than 3m, with some 2m of them housed in 200 camps.