Germany and other Western powers have repeatedly called on Assad to step down to put an end to protests against his government, which have triggered a violent backlash from his security forces.
Syrian security forces have killed more than 5,000 people in the past year, according to human rights groups, while the Assad government says more than 2,000 soldiers and security agents have been killed.
"We will adopt further sanctions in Europe, and not just in Europe," Westerwelle said yesterday (21 February) on the sidelines of a meeting of foreign ministers from the Group of 20 economic powers in Los Cabos, Mexico.
"I believe sanctions will be tightened in the next week, because the violence is continuing," he said when asked whether Europe would adopt measures to blacklist Syria's central bank.
Westerwelle declined to name specific sanctions under consideration, but a G20 official at the meeting, speaking on condition of anonymity, said the EU was on course to agree to measures to curb the central bank's ability to operate.
EU diplomats said this month they were working on a new round of sanctions against Syria, which they hope to finalise by 27 February. These would include a freeze on the Syrian central bank's assets as well as on most transactions with it.
Westerwelle said it was time to raise diplomatic pressure against Syria, and received support from the United States and Britain in Mexico, which also urged China and Russia to do more.
"We'll send a clear message to Russia, China and others who are still unsure about how to handle the increasing violence, but are up until now unfortunately making the wrong choices," US Secretary of State Hillary Clinton told reporters.
Beijing and Moscow angered the West and Arab states this month when they vetoed a draft UN Security Council resolution that backed an Arab plan demanding Assad step aside.
On Monday, the two powers showed support for Assad.
Assad met a senior Russian politician in Damascus, who reiterated Moscow's backing for his self-styled reform program and spoke out against any foreign intervention in the conflict, Russian and Syrian news agencies reported.
China accused Western countries of stirring up civil war in Syria and two Iranian warships docked at a Syrian naval base, underscoring rising international tensions over the crisis.