BERLIN — In a spectacle that a leading weekly likened to a slapstick movie, Germany’s military, especially its air force, has repeatedly stumbled in recent days as it tried to ratchet up its international involvement by delivering personnel and matériel to forces battling Islamic extremists in Iraq and aid supplies to Africa to ease the Ebola crisis.

By Monday, when the latest failure of Germany’s limited air capabilities became known, politicians were demanding explanations from Ursula von der Leyen, the country’s defense minister, and pondering aloud the possible revision of what has long been a political no-go: raising the budget for defense spending.

Ms. von der Leyen is among German leaders who in recent months have championed a more active role for the country in international crises. One striking example was the decision this month to send arms to Kurdish and Iraqi security forces, which broke a longstanding taboo on Germany’s dispatching of weapons to a conflict zone.

But weaknesses began to emerge last week, when a plane that was taking six German paratroopers to Iraq — to help train Kurdish security forces on nearly $900 million worth of weaponry — ended up stuck in Bulgaria for two days without authorization to enter Iraq.