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It is not clear when Mr Ekpendu, who has not yet reacted to the report, will face the MPs.
Nigerian officials often travel in large convoys, forcing other motorists to make way. There have been frequent accusations that those who refuse to pull over are assaulted.
All heads of security agencies in the parliament have also been summoned to explain why they failed to protect the lawmaker.
Beware of blue lights - Naziru Mikailu, BBC News
Driving along the roads of Nigeria's major cities, it is common to see a large convoy of senior government officials moving at high speed.
They often show scant respect for traffic rules.
When you spot the blue lights flashing behind your car or hear the sirens, you know that you must give way regardless of the situation.
This often causes terrible accidents and lead to abuses of ordinary motorists.
The country was shocked in September last year when the officials in the motorcade of a state governor allegedly assaulted a woman and her two children on a highway for not vacating the road for the politician's convoy on time.
In most cases the individuals or the politicians and security forces responsible for these large convoys get away with it.
After coming to office last year, President Muhammdu Buhari ordered his convoy and security aides to abide by traffic rules and respect other motorists.
But it appears that the president's action is yet to convince some other top officials to change their minds.