Kofi Annan holds talks with Syria's Assad

U.N.-Arab League Special Envoy Kofi Annan holds a press conference in the Syrian capital Damascus on July 9, 2012, after meeting with President Bashar al-Assad.

(CBS/AP) DAMASCUS - In a last-ditch attempt to salvage the peace effort in Syria, U.N.-Arab League Special Envoy Kofi Annan met for two hours with Syrian President Bashar al-Assad, and said the two had agreed on an approach to end the violence.

Speaking to reporters in the Syrian capital Monday, Annan did not disclose details.

"We discussed the need to end the violence and ways and means of doing so," Annan said. "I also stressed the importance of moving ahead with a political dialogue, which the president accepts."

It was Annan's third visit to Syria since the crisis began.

Annan is the architect of an international plan to end Syria's 16-month old crisis which started with largely peaceful protests calling for reforms but which has transformed into a bloody insurgency to topple Assad.

Annan's six-point plan was to begin with a cease-fire in mid-April between government forces and rebels, but the truce never took hold.

Activists say more than 14,000 people have died since the uprising began.

The former U.N. secretary-general acknowledged in a recent interview that the international community's efforts to find a political solution to the escalating violence in Syria have failed.

Kofi Annan: Syria peace effort failing

In a TV interview broadcast Sunday, Assad said Annan's peace plan should not be allowed to fail.

But he also accused the United States of undermining peace talks by supporting Syrian opposition groups.

"They offered an umbrella - political support - to those gangs, to create instability, to destabilize Syria," he said.

He also accused Saudi Arabia, Qatar and Turkey of supplying arms and money to the rebels trying to overthrow him.

Assad also said he believes a majority of Syrians support him, and he will not step down. "A president should not run away from a challenge, and we have a national challenge right now in Syria," Assad said. "A president shouldn't escape the situation."

In a show of force, Syria began large-scale military exercises Sunday to simulate defending the country against outside "aggression."

On "Face the Nation" Sunday, Sen. John McCain accused the Obama administration of not doing enough to remove Assad from power.

"My question is, to the Secretary of State and the President of the United States is, how many more have to die before we take action to help these people with other nations?"

McCain: U.S. leadership on Syria "shameful and disgraceful"

Secretary of State Hillary Clinton said Assad will be gone soon enough.

"The future to me should be abundantly clear to those who support the Assad regime - the days are numbered," Clinton said at a press conference in Tokyo.

Clinton on Syria: Sand running out of the hourglass
Clinton: "Friends of Syria" must unite to stop Russia, China "blockading" progress