(CNN) -- U.N.-Arab League envoy Kofi Annan is weighing an invitation to meet with President Bashar al-Assad in Syria, a senior U.N. source said Thursday, the same day that a deadly blast in Damascus drew widespread condemnation and finger-pointing in the volatile nation.
The invitation was extended via Syrian Foreign Minister Walid Moallem over the past few days, and thus wasn't necessarily tied to Thursday's attack.
The former U.N. secretary-general brokered a cease-fire deal, to which key parties had ostensibly agreed, that was to take effect April 12. Since then there have been some calmer days, but violence has continued: The Local Coordination Committees of Syria, a network of opposition activists, reports at least 1,025 people have been killed -- some of them executed and tortured to death -- since that date.
Syria has been mired in unrest since March 2011, when al-Assad's forces began cracking down on anti-government demonstrators. The United Nations has said more than 9,000 people have been killed nationwide since then, while opposition groups put the toll at more than 11,000.
Even amid all that bloodshed, Thursday was a milestone day.
Syrian authorities said two "booby-trapped cars" filled with more than a ton of explosives blew up at an intersection in the densely populated Damascus neighborhood of Qazzaz as people headed out to start their days.
State television showed panicked residents running down bloody streets strewn with body parts and burned cars. The government said the blasts led to scores of car crashes.
"The place looks like hell," a man told Syria state TV, describing "burned corpses all over the place" and people dead in their homes.
The opposition Syrian Observatory for Human Rights said at least 59 died, and the nation's intelligence agency building was destroyed in what it called the single deadliest attack since Syrian forces began cracking down on dissenters in March 2011.
Syria's U.N. ambassador Bashar Jaafari said 56 civilians and security forces died and 372 suffered "grave injuries in what he called a "cowardly" attack in the vicinity of four schools.
Al-Assad's government faults "terrorists," the term it uses to describe the opposition and rationalize security forces' crackdown.
But two groups part of that effort -- the Syrian National Council and the National Coordination Committee for Democratic Change -- blamed the regime. Opposition members have accused al-Assad's forces of high-profile bombings in the large cities of Aleppo and Damascus in recent months to undermine the resistance's credibility.
"This is a government-planned attack," said Ausama Monajed, the adviser to the Council's president. "We are in touch with the armed resistance."
Brig. Gen. Moustafa el-Sheikh, head of the rebel Free Syrian Army's military council, said that "no other parties in Syria ... are technically capable of making such a huge explosion, except for the regime itself."
"Not even al Qaeda can do that," he said.
Analysts said the attack raises concerns about the presence of jihadist elements in Syria, noting the Damascus strike resembles suicide car bombings during the sectarian civil warfare prevalent in the last decade in Iraq.
Bill Roggio, an analyst on terror and military issues, said he believes the attack "very likely" was carried out by an al Qaeda-linked militant group called the Al Nusrah Front for the People of the Levant, which has claimed credit for recent suicide attacks in Damascus and Aleppo.
He said another jihadi group called the Al Baraa Ibn Malik Martyrdom Brigade also has surfaced, and that al Qaeda in Iraq has had a "strong presence" in Syria. Foreign fighters entered Iraq through Syria during the war there.
Jeffrey White, a defense fellow and analyst at the Washington Institute for Near East Policy, concurred that Thursday's suicide strike is "coordinated (and) very destructive," much like what al Qaeda elements in Iraq claimed credit for.
While Roggio, the managing editor of the Long War Journal blog, called it "very concerning" that opposition groups have "ignored" or denied the activities of terrorist groups, White said opposition members aren't necessarily ignoring an uptick in terrorist activity.
Rather, they feel al-Assad's regime is using "jihadists and al Qaeda types" that it was tied to during the Iraq war. There are people in the Syrian opposition, he said, who call the Al Nusrah Front a Syrian government organization.
"The opposition guys are saying the regime still controls them. When they want them to do something, they order them up," White said.
Noting that the attack "is not typical of Free Syrian Army-type actions such as ambushes, bombings of regime vehicles, targeted killings, and attacks on checkpoints," White said there is no way to know definitively who is responsible. But he said he doubts the government is behind attacking "pillars of the regime."
But Rafif Jouejati, spokeswoman for the opposition Local Coordination Committees of Syria, insists that al-Assad's forces could be "stepping up its attacks on civilians."
"The regime thugs who have been scrawling 'Assad or we burn down the country' all over Syria appear to be making good on the promise," said Jouejati, whose group issued a statement decrying the "terrorist explosions" that it believes were meant to "lure the international community ... to adopt the regime's vision."
Or, she said, the government could be losing control and "allowing a dire situation to get worse."
"The very chaos that some were afraid would reign in the country post-Assad is being perpetuated by the regime today," she said. "If it was indeed an external group, the regime is clearly not in control of the situation, as they have traditionally claimed to be."
The bombings weren't the only violence reported Thursday in Syria.
Another 20 people died in the Middle Eastern nation at the hands of "regime forces," the Local Coordination Committees said, including nine in Homs and three apiece in Aleppo and the Damascus suburbs. The group reported government attacks Thursday night such as mortar-fire aimed at Old Homs, heavy gunfire in parts of Daraa and shots fired at demonstrators in Damascus.
There was also continued movement on the diplomatic front.
That included a speech by Jaafari to a meeting of fellow U.N. diplomats in New York; he insisted that sending or smuggling weapons into Syria -- presumably for opposition fighters -- undermines the peace efforts pushed by Annan.
He added that Security Council members will soon get a "list of 12 foreign terrorists" -- including "French, British and Belgian terrorists" -- killed in Syria, according to a SANA report.
In China, meanwhile, the foreign minister and a Communist Party leader met Thursday with a delegation from the Syrian National Council, the opposition group said in a statement. The council said the meeting with Foreign Minister Yang Jiechi -- in which its group tried to "clear up misconceptions China had about the Syrian revolution" and stressed its commitment to Annan's peace plan -- lasted two hours and 10 minutes, twice as long as planned.
CNN's Hala Gorani, Amir Ahmed, Arwa Damon, Elizabeth Joseph and Tracy Doueiry contributed to this report.