Jonathan spent three hours in Maiduguri, capital of Borno State, meeting with survivors of what is thought to be the worst attack in Boko Haram's six-year insurgency.
On a visit to a camp sheltering about 5,000 people who fled the January 3 attack on Baga in northern Borno, he said his security chiefs had promised "all the areas under the control of Boko Haram will soon be recaptured".
"I want to assure you that you will soon go back to your houses," Jonathan, who is seeking a second term in elections next month, told some of the displaced.
The attack on Baga, part of an upsurge in violence ahead of February's presidential and parliamentary polls, is feared to have killed hundreds, if not more.
Amnesty International and Human Rights Watch published separate satellite images Thursday that appeared to show massive destruction in both Baga and the adjacent town of Doron Baga, which is home to a regional military base.
Amnesty's images showed aerial shots of the towns on January 2 — the day before the attack — and January 7.
The group said the images suggested "devastation of catastrophic proportions", with more than 3,700 structures, mostly in Doron Baga, damaged or completely destroyed.
HRW said 11 percent of Baga and 57 percent of Doron Baga was flattened, most likely by fire.
HRW said the exact death toll was unknown and quoted one local resident as saying: "No one stayed back to count the bodies.
"We were all running to get out of town ahead of Boko Haram fighters who have since taken over the area."
Nigeria's military, which often downplays death tolls, said that 150 died and dismissed as "sensational" claims that 2,000 may have lost their lives in the attacks
US Secretary of State John Kerry accused the Islamist insurgents of a "crime against humanity".
The "evil" Boko Haram is a serious threat "to all of our values", Kerry said during a visit to Bulgaria, adding he had spoken to his British counterpart Philip Hammond about the possibility of "a special initiative" on Nigeria. He did not give details.
Amnesty said Boko Haram reportedly targeted civilians who had helped the army after the fighters overran a Multinational Joint Task Force base for troops from Nigeria, Niger and Chad who have been involved in operations against them.
Cameroon announced Thursday that neighbouring Chad will send troops to aid his country's army fight Boko Haram, though no date for the deployment or size of the contingent was given .
Harrowing testimony has emerged from survivors of the killings in Borno, about the scale and brutality of the assault.
Amnesty said on Thursday it had received accounts of the attackers of firing indiscriminately, killing small children as well as a woman who was giving birth.
"Half of the baby boy (was) out and she died like this," an unnamed witness was quoted as saying.
A man in his fifties added: "They killed so many people. I saw maybe around 100 killed at that time in Baga. I ran to the bush. As we were running, they were shooting and killing."
Witnesses who spoke to AFP described seeing decomposing bodies in the streets.
Amnesty cited reports of women being rounded up and detained at a school.
"The deliberate killing of civilians and destruction of their property by Boko Haram are war crimes and crimes against humanity and must be duly investigated," Amnesty added.
Meanwhile Gordon Brown, UN special envoy for education, urged the world to condemn the use of young girls as suicide bombers by Boko Haram, calling it "barbaric."
At least 19 people were killed last Saturday when a young girl, thought to be aged about 10, blew herself up at a crowded market in the northeast Nigerian city of Maiduguri, the Red Cross and local vigilantes said.
Jonathan's visit to Maiduguri — his first since March 2013 — was shrouded in secrecy and came after a previous trip to the restive region in May last year was cancelled at the last minute.
Nigeria's leader has come under fierce criticism for his failure to crush Boko Haram's bid to establish a hardline Islamic state in northeast Nigeria. Over 13,000 people have been killed in the violence since 2009.
The bloodshed has raised concerns about the security of next month's elections.
Nigeria's electoral commission said voting was "unlikely" to take place in rebel-controlled areas but that arrangements were being made to allow hundreds of thousands of displaced people to cast their ballots.