Polling had to be abandoned last week after election material failed to reach many areas.
Security is tight following sporadic violence in the campaign. Several people were hurt on Saturday in a blast at a polling station in the north-east.
About 73.5m are registered to vote, with President Goodluck Jonathan's PDP battling to maintain its majority.
'Ready for democracy'
The BBC's Caroline Duffield in Lagos says there are tight security controls across the country, with many towns and cities appearing deserted, borders closed and flights grounded.
The polling procedure began at about 0800 (0800 GMT) on Saturday, with registration of voters to avoid irregularities. Polling stations started taking votes at about noon.
First indications were that, although some officials failed to turn up on time, the organisation was better than last week.
Voting - for 360 seats in the lower chamber, and 109 in the Senate - had already begun last Saturday, and millions were queuing, when it was discovered that ballot papers were missing in some parts of the country, prompting delays due to the difficulty of replacing ballot papers.
Various issues have resulted in three separate announcements of postponements, while the elections for president and state governors have also been set back.
Despite the delays, our correspondent says, many people see these polls as a chance for Nigeria to escape the troubled days of vote rigging and violence that have plagued previous elections held since the end of military rule in 1999.
Politically the stakes are high, she says, with this being seen as a test of whether this government can hold a credible election.
One voter in Lagos, Mukaila Odukoya, told Reuters: "We want to show the rest of the world that we are ready for democracy. This one is going to be far, far better than the past."
Mr Jonathan is widely expected to win the forthcoming presidential poll, but his People's Democratic Party is under pressure to stave off a cut in its majority in the National Assembly.
The presidential elections have been put back a week to 16 April, with polls to choose the 36 powerful state governors now to be held on 26 April.
The campaigns have been marred by violence.
A number of people were injured on Saturday in an explosion at a polling booth in the north-eastern city of Maiduguri, officials said.
On Friday, a bomb blast at the election commission's office in Suleja, 20 km (12 miles) from the capital Abuja, killed at least six people.
Also on Friday, in the north-eastern state of Borno, gunmen shot dead four people at a police station where election officials were preparing voting materials.
source : bbc.co.uk
