U.S. Secretary of State John Kerry says the U.S. and Russia are "very pleased" with the progress made so far in destroying Syria's chemical weapons stocks.

Kerry, speaking at a press conference with Russian Foreign Minister Sergey Lavrov, said Syrian President Bashar Assad's regime deserves credit for its compliance with the U.N. Security Council resolution calling for the elimination of the weapons. Kerry said Assad was not off the hook, but needs to continue to comply with U.N. demands.

He said it was "extremely significant" that the first weapons were destroyed Sunday, just a few weeks after the resolution passed the U.N. "It is a good beginning, and we should welcome a good beginning," Kerry said.

The U.S. and Russia also agreed to press the UN to set a date for a Syria peace conference sometime in the second week of November, Kerry said.

"We will urge a date to be set as soon as possible," Kerry told reporters at a joint news conference with Lavrov.

Kerry and Lavrov met Monday on the sidelines of an economic summit on the Indonesian resort island of Bali. Their meeting represented the first high-level talks between the two nations since they sealed a deal to secure and destroy Syria's chemical weapons.

On Sunday, international inspectors began the enormous task of destroying Syria's stockpile of chemical weapons and the machinery used to create it, a United Nations official said, racing to meet a tight deadline to eliminate Assad's chemical weapons program.

The disarmament experts arrived in Damascus last Tuesday to carry out their mission under a UN Security Council resolution to dismantle and ultimately eliminate Syria's estimated 907-tonne arsenal. Their first goal in the undertaking is to scrap the Assad regime's capacity to manufacture chemical weapons by Nov. 1.

By the end of the day Sunday, a combination of both weapons and some production equipment would be put out of order, a UN official who works alongside the inspectors said.

"Today is the first day of the phase of destruction and disabling. Verification will also continue," the official, speaking on condition of anonymity because of the sensitivity of the matter. "The plan was that two types categories of materials would be destroyed: one is equipment for making (weapons) — filling and mixing equipment, some of it mobile, and some it static. The other is actual munitions."

He could not provide further details, nor say where the destruction took place.

Working amid civil war

It is just the first step in a mission that has the ambitious task of eliminating Syria's entire chemical arms production capability and stockpile by mid-2014. That's the tightest deadline that experts from the Organization for the Prohibition of Chemical Weapons (OPCW) have ever faced, and this mission marks the first time they have operated in a country at war.

Developed during the 1980s and 1990s, Syria's chemical arsenal is believed to contain mustard gas and the nerve agents sarin, VX and tabun.

An advance team of 19 OPCW (Organization for the Prohibition of Chemical Weapons) experts arrived in the country last week to lay the foundations for a broader operation with nearly 100 inspectors.

Those already in the country have been double-checking Syria's initial disclosure of what weapons and chemical precursors it has and where they are located, while others have been planning logistics for visits to every location where chemicals or weapons are stored — from trucks loaded with weapons up to full-on production sites.

Inspectors can use any means to destroy equipment, including crude techniques like taking sledgehammers to control panels or driving tanks over empty vats. But the second phase — destroying battle-ready weapons, is more difficult, time-consuming and expensive. It can be done by incinerating materials in sealed furnaces at ultra-high temperatures, or by transforming precursor chemicals or diluting them with water.

Questions remain over how inspectors will achieve those goals while working in the midst of Syria's civil war. Underscoring the perils they face, four mortar shells landed in the once-touristic Christian quarter of Bab Touma and al-Qasaa, killing at least eight people, said Syria's state news agency. It was unclear whether any inspectors were close to the explosions.

100,000 killed since 2011

The disarmament mission stems from a deadly Aug. 21 attack on opposition-held suburbs of Damascus in which the UN has determined the nerve agent sarin was used. Hundreds of people, including children were killed. The U.S. and Western allies accuse the Syrian government of being responsible, while Damascus blames the rebels.

The Obama administration threatened to launch punitive missile strikes against Syria, prompting frantic diplomatic efforts to forestall an attack. Those efforts concluded with September's unanimous UN Security Council resolution endorsing the elimination of Syria's chemical weapons.

In an interview in a state-run newspaper Sunday, Assad said the Syrian regime began producing chemical weapons in the 1980s to "fill the technical gap in the traditional weapons between Syria and Israel."

He said production of chemical weapons was halted in the late 1990s, but provided no further information.

Syria's conflict evolved from largely peaceful protests in March 2011. In the two years since, it has since has laid waste to the countries' cities, shattered its economy, killed around 100,000 people and driven more than 2 million people to seek shelter abroad.

The violence affects nearly every corner of Syria, which has become a patchwork of rebel-held and regime-held territory.

With files from Reuters