"They both agreed that we've got to work together," the official said.
"Her message to him was: 'We've got to start working together to help the Syrians with Syria's political transition strategy. And I want our people to work together on ideas in Moscow, Europe, in Washington, wherever we need to'."
At a ministerial meeting in the Qatari capital Doha, Annan warned: "The spectre of an all-out war with a worrying sectarian dimension grows by the day.
"The situation is complex and it takes everyone involved in the conflict to act responsibly if the violence is to stop. But the first responsibility lies in the Syrian government and President Assad," he said.
Up to 300 unarmed UN military observers have deployed in Syria since a putative ceasefire brokered by Annan went into effect in April as part of Annan's six-point peace plan.
The plan also stipulated that the army had to pull out of towns and cities.
"I told Assad he must act now to implement all points of the plan, and must make bold and visible steps immediately to radically change his military posture and honour commitments to withdraw heavy weapons and cease all violence," Annan said.
He had also told Assad to release detainees, open Syria to international humanitarian aid and allow freedom of expression, he added, as "this is essential to demonstrate his seriousness to the Syrian people and the international community."
Earlier, the Arab League's ministerial committee on Syria had called on Annan, the UN-Arab League envoy on the crisis who met Assad earlier this week, to set a deadline for the terms of his peace initiative to be met.
"We request Mr Annan to set a time frame for his mission because it is unacceptable that massacres and bloodshed continue while the mission is ongoing indefinitely," Qatari Prime Minister Sheikh Hamad bin Jassim Al-Thani said.
"We demand the UN Security Council refer the six-point (Annan plan) to Chapter VII so that the international community could assume responsibilities," he added.
Chapter VII outlines action the Security Council might take, including military force, in response to threats to international peace, breaches of the peace and acts of aggression.
Arab League chief Nabil al-Arabi also said he had asked the Security Council to take strong action to protect civilians in Syria but did not raise the question of intervention.
"I sent a letter to the UN Security Council asking it to undertake all necessary measures to protect the Syrian people," Arabi told AFP shortly before the opening of the Doha meeting.
Afterwards, Arabi told reporters the ministers "did not request a military action."
The Arab ministers also asked Arabsat and Egypt's Nilesat to "take the necessary measures to stop the broadcast of both official and unofficial Syrian satellite channels."
Syrian television quoted an information ministry statement as calling the decision "aggression against the freedom of the press."
In Syria itself, troops conducted raids in search of anti-regime militants and clashed with rebels in several regions. The Syrian Observatory for Human Rights reported at least 39 people killed -- 22 soldiers, a policeman, 15 civilians and one deserter.
It also reported fierce fighting between government forces and rebels in the town of Ariha in Idlib province, with reports of heavy regime losses.
Tensions also spilled over into neighbouring Lebanon. Clashes between pro- and anti-Damascus gunmen killed 10 people and wounded more than 31 in the northern city of Tripoli.
The London-based observatory says as many as 2,300 of the more than 13,400 people killed in Syria since the uprising against Assad's regime began in March 2011 have died since the so-called ceasefire began on April 12.
Because of the worsening violence and Assad's failure to meet commitments under an agreed peace plan, the United States has warned that it may not agree to renew the UN observer mission when its mandate expires on July 20.