The 14-minute video of Abubakar Shekau seen on YouTube belittled Jonathan for saying two weeks ago that the security situation would be under control by the middle of this year.
"You, Jonathan, cannot stop us, instead we will devour you in the three months like you are boasting," Shekau said in the video entitled "message to Goodluck Jonathan", flanked by four masked men holding rifles.
"We are proud soldiers of Allah, we will never give up as we fight the infidels. We will emerge as winners ... we will finish you and end your government," Shekau said, speaking in Arabic and in the Hausa-language spoken in northern Nigeria.
Shekau has now posted two videos and one audio recording on the Internet this year, suggesting he wants to solidify his position as the sect's leader.
There were brief efforts last month at dialogue using mediators between the government and the sect but details were leaked to the press and talks collapsed. A Boko Haram spokesman has since said they will never negotiate.
Although almost daily small scale shootings continue in the northeast, a military crackdown and some high profile sect arrests in recent weeks prompted a pause in big coordinated attacks, since 186 people were killed in bomb and gun strikes in Nigeria's second city of Kano in January.
It was hoped the sect had been weakened but on Easter Sunday a car bomb killed at least 36 people after security officials prevented the vehicle entering a church compound in the northern town of Kaduna and another large car bomb was discovered undetonated in Kano.
No group has taken responsibility for the Kaduna attack but security experts believe Boko Haram may want to distance itself from the strike, which appeared to fail to hit its target and killed many Muslims.Shekau said in Thursday's video that Boko Haram would continue to target anyone who killed its members or aided in their arrest, whether they be Christian or Muslim.
Meanwhile, barely one week after the killing of nine Igbos and three Kanuris at the Maiduguri Monday Market, unknown gunmen, again, stormed the market on Thursday, killing one person and injuring many others.A source in the market told Nigerian Tribune that just as it happened last week, the gunmen, after opening fire at their target, also made away with huge sums of money.
Also confirming the incident, the spokesman for the Joint Task Force (JTF) on Operation Restore Order in Borno, Lieutenant-Colonel Shamsu Musa, said, “It is true one person was shot dead by unknown gunmen in Monday Market, Maiduguri city at about 12.45 p.m.”According to him, the general area where the incident happened had been cordoned off and searched.
Lieutenant-Colonel Shamsu also said that foot patrol had been intensified to avoid stampede, as troops also assisted people to get out of the market while effort was ongoing to arrest the culprits.
He said, so far, no one was reported injured by their record, no weapon was found or recovered and no arrests made.
Officials of the Maiduguri Monday Market were not available for comments, as people were seen rushing back home at the time of filing this report.