The bases belonged to the FSA's Supreme Military Council, led by Gen. Salim Idris, a secular-minded, Western-backed moderate.
Their takeover by the Islamic Front, a new alliance of six of the most powerful Islamic rebel groups in Syria, was an embarrassing setback for Idris, who has seen his influence greatly diminished by the rise of al-Qaida affiliated militants flush with cash, weapons and battleground experience.
"We have seen the reports that Islamic Front forces have seized the headquarters in question and warehouses belonging to the Supreme Military Council, and we're obviously concerned by those reports," White House spokesman Josh Earnest said in announcing the suspension. "We're still gathering facts and consulting with Gen. Idris and the Supreme Military Council staff to inventory the status of U.S. equipment and supplies that have been provided to the SMC."
State Department spokeswoman Jen Psaki said U.S. assistance "continues through other neighboring countries to other parts of Syria."
Britain's Foreign Office said it "will not be making any deliveries of equipment" to the FSA while it investigates those attacks. It said it intends to resume assistance as soon as conditions on the ground allow for its "safe delivery."
"The decision is a belated but clear recognition by the Americans and its allies of the collapse of the Syrian opposition umbrella and its armed wing," said Fawaz A. Gerges, director of the Middle East Center at the London School of Economics.
Turkey said it was shutting its side of the border in response. A statement issued by the ministry of customs and trade confirmed the closure Tuesday, saying the Syrian side of the Bab al-Hawa crossing was now in the hands of the Islamic Front.
Capt. Islam Alloush, a military spokesman for the Islamic Front, denied fighters of the group had forcefully taken over the SMC warehouses.
"This is a lie," he told The Associated Press in an interview over Skype. He said fighters from the Front, which include the ultraconservative Ahrar al-Sham faction, had received a call from Idris' office asking for assistance after they came under attack from unknown gunmen.
When the fighters reached the area, they found the warehouses emptied and the guards and officers of the SMC had fled, he said.
Idris and other FSA officials could not be immediately reached for comment.
More than 100,000 people have died in Syria's civil war, now in its third year. With just about a month to go before the start of internationally brokered peace talks to end the civil war, Assad's forces have stepped up a punishing offensive against rebels in a mountainous region near the border with Lebanon.
The fractured opposition movement has been losing ground militarily as rebel factions turn their guns against each other, and the rise of al-Qaida linked factions has diminished international confidence in the rebels and undermined the battle against Assad.
Some of the six rebel groups in the Islamic Front were once part of the FSA. The Front seeks to establish an Islamic state in Syria but its officers insist they are not allied with al-Qaida affiliates like the Islamic State in Iraq and the Levant and Jabhat al-Nusra, or Nusra Front.
A Washington-based U.S. official said members of the Islamic Front are not considered to be terrorists, but not exactly moderate. The U.S. fears that segments of the group have been in contact with al-Qaida elements and are sympathetic to them, he added.
The official spoke on condition of anonymity because he was not authorized to speak publicly about the matter.
Britain's Prime Minister David Cameron warned against the idea that all of Syria's opposition members are extremists and stressed the need to continue working with its moderate members.
"We must not allow this argument to develop that the only opposition in Syria is an extremist opposition," he told British lawmakers Wednesday, because that will only become reality if "we stop working with those who care about democracy and the future."
The White House stressed that it was continuing to provide humanitarian assistance, which is distributed through organizations such as the United Nations.
Tens of thousands of Syrian refugees were hunkered down against the wintry weather in the region, some in flimsy, plastic tents.
In dozens of informal refugee settlements near the border with Syria, refugees were piling up extra layers of plastic bags and tarps supplied by the UNHCR to try to reinforce their tents. Water seeped into some tents while high winds blew away others.
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Butler reported from Istanbul. Associated Press writers Matthew Lee and Bradley Klapper in Washington, Cassandra Vinograd in London and Barbara Surk in Beirut contributed to this report.