Albania Friday rejected a US request to host the destruction of Syria's chemical weapons, in a new setback for the internationally-backed disarmament plan three weeks after Norway also said no.

"It is impossible for Albania to take part in such an operation... as it has no capacity" to carry out such a task, Albanian Prime Minister Edi Rama told reporters.

More than 4,000 people opposed to the destruction of the chemical arsenal on Albanian soil cheered Rama's announcement, which was broadcast live on giant screens on Tirana's main square.

Rama said that the United States had asked Albania to "contribute to the destruction of chemical weapons".

"Our response was 'yes, in principle'. We are ready to engage in this mission, but we do not have the capacity," Rama said.

He said the decision was "very difficult".

In a statement issued immediately after Rama's press conference, the US embassy said Washington "appreciates that the government of Albania gave serious consideration" to the issue.

"We respect the Prime Minister's decision... We remain confident that we will complete elimination of the program within the timeline agreed upon," the embassy said.

NATO member Albania, along with France and Belgium, had been mooted as a possible host for site for the dismantling of Syria's entire chemical arsenal, estimated at about 1,000 tonnes.

Rama's Socialist-led government, in office since September, had over the past week faced growing street protests over the prospect.

Protestors dispersed in Tirana and other Albanian towns after Rama's announcement.

Hundreds of people spent the night outside Albania's seat of government, while thousands of protesters gathered in towns across the country.

Protesters carried placards saying "No to chemical weapons", "We love the United States, but we prefer Albania" and "We want oxygen, not sarin gas".

Protest organisers, the non-governmental Alliance Against Waste Import, said some 35,000 people had signed a petition urging the authorities to reject the US request.

"Albania is no one's dumping ground. I am a mother of two and I am here for their future," said Suzana Agimi, a 41-year-old Tirana university professor who joined the protest with her twin daughters.

Businessman Bujar Topi, 34, warned that "nobody will come to invest in the country fearing risks of chemical weapons".

"If chemical weapons are brought here, our only choice is to leave Albania," said 18-year-old student Admir Suli, who wore a military gas-mask like many protesters.

Analyst Lutfi Dervishi said Albania had so far done "everything the United States wants".

"Albania is a small country that has always needed US support. In turn, Washington sees Albania as its closest strategic ally in the region," Dervishi told AFP.

'The load is too large for Albania'

But Dervishi warned that the country, although "indebted" to Washington for its support for Albania's NATO entry in 2009, public pressure on Rama's two-month-old government was very strong.

"Albania has never said no to the United States but this time the load is too large for a small country and its capabilities," said Dervishi.

In Durres, several hundred people blocked the entries to the city's port, warning they would form a human barrier to prevent the unloading of chemical weaponry on Albania's soil.

In 2007, OPCW confirmed that formerly communist Albania had destroyed its own stockpile of Cold War chemical weapons.

Under a UN Security Council resolution passed in September, Syria's weaponry has to be destroyed by June 30, 2014.

Oslo last month also announced it would not be able to host the destruction.

Norway and Denmark have however said they will provide ships to take the chemicals out of Syria, with Denmark saying it would also provide a personal protection team for international inspectors.

In The Hague, the Organisation for the Prohibition of Chemical Weapons (OPCW) met Friday to approve a final timetable for destruction, according to the terms of a US-Russian deal that headed off US military strikes on President Bashar al-Assad's regime.