A coastal ranger from the Norwegian special naval force group looks on as Norwegian frigate HNoMS "Helge Ingstad" secures the Danish and Norwegian cargo vessels "Taiko" and "Ark Futura" in Latakia in this handout photo from January 27, 2014 released to Reuters on January 30, 2014 by the Norwegian Armed Forces.
US Secretary of State John Kerry has asked Russia to press its ally Syria into speeding up the removal of chemical weapons.
The US says only about 4 percent of chemical weapons declared by the Syrian government have so far been removed.
Kerry raised the issue with Russian Foreign Minister Sergei Lavrov on the sidelines of the Munich Security Conference, officials said.
Syria's chemical weapons are due to be removed and destroyed by June 30.
Under the terms of the UN-backed plan, Syrian authorities are responsible for packing and safely transporting the chemical weapons to the Mediterranean port of Latakia.
The first consignment of 16 tonnes, from two Syrian sites, left Latakia on January 7.
A further shipment left on January 27, according to the Organisation for the Prohibition of Chemical Weapons (OPCW).
"Secretary Kerry pressed Foreign Minister Lavrov to push the regime for more progress on moving the remaining chemical weapons within Syria to the port in Latakia," the US State Department official said.
Washington considered progress so far to be "unacceptable", the official added.
The OPCW, which is overseeing the destruction of Syria's chemical arsenal, has been meeting in The Hague to discuss the operation's progress.
Earlier this week, the US ambassador to the OPCW, Robert Mikulak, said "the effort to remove chemical agent and key precursor chemicals from Syria has seriously languished and stalled".
"The spotlight now is on Syria to proceed without further delay to comply with its obligations and make this effort a success," he added.
Denmark and Norway are providing cargo ships and military escorts to take them to Italy, where they will be loaded onto a US Maritime Administration cargo ship, MV Cape Ray.
The materials will be destroyed in international waters.
Correspondents say failure to eliminate the weapons could expose Syria to the threat of sanctions, although these would have to be supported in the UN Security Council by Russia and China which have so far refused to back such measures.
Also in Munich, Kerry and Lavrov met UN Secretary General Ban Ki-moon and UN envoy to Syria Lakhdar Brahimi to discuss the lack of progress in the Syria peace talks in Geneva.
The talks ended on Friday with rival Syrian delegations trading insults.
Brahimi later told a panel on Syria at the conference: "We have failed somewhere.
"We can say it is an intractable problem, it is difficult. But somewhere there is a failure."
However, Brahimi said he hoped the talks would resume in Geneva on 10 February in a "more constructive" mood.
The Munich Security Conference is an annual event held to discuss military and political affairs.