A senior Iraqi official said all the crossings on Syria's eastern frontier had been seized. At one point, two Turkish posts were also in rebel hands.
The push came a day after a bomb claimed the lives of three senior defence officials in Damascus.
At the UN, negotiations are under way on extending the mandate of the observer mission in Syria,
The mandate for the mission is due to expire on Friday.
There are almost 300 UN observers in Syria, but the mission suspended most of its monitoring activity in June, because of the risk from increasing violence.
The US says it might consider a final brief extension of the monitors work, but warned that it could not pin its policy on an unarmed mission.
The UK is said to be proposing an extension for a "final 30 days".
The major Abu Kamal crossing on the Euphrates River in the east was captured after a clash with government forces, opposition activists said.
More than 20 Syrian soldiers and their commander were killed when a remote army outpost in the far north-east was attacked, Associated Press news agency reported.
Iraq's government, seen as sympathetic to President Bashar al-Assad, has threatened to shut its side of the border and one official told Reuters news agency that it was closing the Abu Kamal crossing.