About one million Syrians are going short of food, most of them in conflict zones, due to government restrictions on aid distribution, the United Nations said on Tuesday.
Bread and fuel particularly are in short supply.
The WFP is unable to step up assistance as only a handful of aid agencies are authorised to distribute relief goods in Syria, where more than 60,000 people have been killed during 21 months of conflict.
"Our main partner, the (Syrian Arab) Red Crescent, is overstretched and has no more capacity to expand further," Byrs told a news briefing in Geneva.
Long lines in front of bakeries are now normal in many parts of Syria and there are reports of shortages of wheat flour in most parts of the country due to damage to mills, most of which are located in the embattled Aleppo area, she said.
"WFP is making arrangements to import fuel for humanitarian use, to resolve the impact of a significant fuel shortage throughout the country that has been affecting the agency's ability to move food on time - from the port to packaging facilities - and to find trucks to dispatch food for distribution," she said.
The United Nations last month appealed for $1.5bn to help save the millions of Syrians suffering from what it called a dramatically deteriorating humanitarian situation.
Four million people in the country need urgent humanitarian aid, including an estimated 2 million displaced from their homes by fighting between the forces of President Bashar al-Assad and rebels trying to topple him.
The number of registered Syrian refugees has leapt from 500,000 to nearly 600,000 in the past month, U.N. figures show.