The request was made in two letters presented to the House of Representatives and the Senate in Nigeria's capital, Abuja.
Jonathan's letter claimed "considerable successes in containing the activities of the terrorist element" but said some security challenges still exist. Jonathan said he expects "normalcy will be fully restored" within another six months.
Boko Haram attacks have killed hundreds of civilians in recent weeks. On October 16, the extremists engaged security forces in a five-hour battle in Damaturu, the capital of Yobe state, in which they burned down an army barracks and four police buildings.
Thousands of troops and police officers deployed in the emergency swiftly forced the extremists out of major urban centers but the campaign, which includes aerial bombardments and ground assaults, has been struggling to flush them out of hideouts in forests and caves.
The uprising, which began in 2009 and has killed thousands, poses the biggest threat in decades to the security and cohesion of Africa's biggest oil producer and its most populous nation of more than 160 million. It is divided almost equally between the mainly Christian south and the predominantly Muslim north.