"I would hope that the council will continue its discussions and hopefully find language that will pull everybody together for us to move forward on this critical issue," Annan told reporters in Moscow after meeting with Russian President Vladimir Putin and Foreign Minister Sergei Lavrov.
The comments came as fighting raged in Damascus for a third day and on the heels of a BBC interview with Syria's former ambassador to Iraq who said he fears Syrian President Bashar Assad is getting ready to use chemical weapons to put down the uprising.
Annan said his discussion with the Russian leader was "very good" as it focused on what measures are needed to end the carnage and how to proceed with a political transition, the United Nations said in a release.
Annan's six-point peace plan has withered as the Syrian military and opposition fighters waged what the International Red Cross has labeled essentially a civil war.
"As I said earlier, we need to do whatever we can to stop the violence, to stop the killing, and the council, I expect, will be sending a message out, that the killing must stop and the situation on the ground is unacceptable," Annan said. "Hopefully, the council will come together in a united manner and press ahead in search of peace."
A representative for Ban Ki-moon said Tuesday the U.N. secretary-general spoke with Lavrov by phone Monday to add weight to the sense of urgency in finding a resolution to the Syrian crisis.
"He called on Russia to use its influence to ensure the full and immediate implementation of the six-point plan and the action group communique, as well as of Resolutions 2042 and 2043 of the Security Council," Ban's representative said in a note to journalists.
The two resolutions dealt with the deployment of independent monitors.
Russia and China, which have strong trade ties with Syria, have wielded their vetoes on the Security Council to block some of the tougher draft resolutions against the Assad regime.
Western countries, including the United States, have been critical of Russia, saying its actions have helped Assad's forces maintain their deadly crackdown on dissidents.
The international diplomatic efforts played out as fierce battles raged in Damascus for a third day Tuesday and opposition activists warned of a major confrontation in the capital.
The Local Coordination Committees of Syria reported several areas of the capital witnessed intense fighting, with one area under mortar attack and others rocked by explosions, CNN reported.
"The battle for Damascus is coming," said Abdulhameed Zakaria, a Syrian army colonel who defected and joined the rebel Free Syrian Army.
The LCC reported warplanes fired on Herak, with at least two rockets striking the southern city.
The Syrian Network for Human Rights and the Damascus Center for Human Rights Studies said they documented 96 deaths across Syria Tuesday -- 40 in Damascus and Rural Damascus, one of whom was identified as Egyptian, 17 in Aleppo, 15 in Homs, and 10 in Deir Ezzor.
The LLC said at least 97 people were killed across Syria Monday, including 30 deaths in Hama alone.
Since the crisis began in March 2011, the United Nations estimates more than 10,000 people have been killed in the violence, but opposition leaders said the death toll is closer to 15,000.
The New York Times reported Syrian security forces have ramped up their response to clashes in Damascus, dispatching helicopter gunships to fight of rebels on the ground.
"Regime forces are threatening to bombard the whole area and telling civilians to evacuate their houses," said a spokesman for activists in Damascus.
The Free Syrian Army issued a statement vowing to spread out attacks across the city, calling the clashes "the volcano of Damascus and the earthquake of Syria."
On Monday, Morocco became the latest country to expel Syrian diplomats, CNN reported. Syria, in turn, declared Morocco's ambassador persona non grata.
A top Syrian diplomat who defected said the Assad regime will use chemical weapons if cornered.
Assad will only be ousted by force, "even if he will have to eradicate the entire Syrian people," former Ambassador to Iraq Nawaf Fares told the BBC in Qatar.
He described Assad as someone with a god complex who believes he and his family "will live forever as rulers of Syria."
He said the Assad family was "clinging to power" and Assad himself had become "a fully fledged criminal like a wounded wolf."
Fares also told the BBC the Assad regime has teamed up with al-Qaida to coordinate major bombings across Syria.
"Al-Qaida is not concerned with the Syrian people or their interests," Fares said. "Al-Qaida is searching for space to move, for support."
U.S. officials have linked al-Qaida to deadly bombings and attacks in Syria for months, mostly through Sunni fighters seeking to topple the Assad regime, not through the regime itself.
U.S. officials have told The New York Times al-Qaida is seeking to exploit the turmoil and reinvigorate its regional ambitions after being sidelined in the initial popular uprisings of the Arab Spring last year.
Assad last week blamed the escalating Syrian violence on a mixture of al-Qaida forces and other foreign terrorists or thugs.
As battles raged, two more officials reportedly defected.
Maj. Gen. Adnan Sillu, the former head of Syria's chemical-weapons program, said in an online video he would now head the opposition Free Syrian Army's joint military leadership.
In addition, Farouk Taha, Syria's ambassador to Belarus until his mission ended six months ago, announced his defection, Syrian National Council sources told Arabic newspaper Asharq al-Awsat.
Celebrity Families of 2014 [PHOTOS]