BRUSSELS—European Union leaders held off issuing a threat to sanction Russians supporting the Assad regime’s siege of Aleppo after objections from Italy, saying instead that all options remained available if the bombing continues.

At the end of a summit meeting that ran past midnight, the bloc’s leaders called for an end to Russian and Syrian attacks on Aleppo, immediate steps to allow the delivery of humanitarian aid to rebel-held parts of the city and the resumption of a peace process.

Italian Prime Minister Matteo Renzi strongly opposed including a sanctions threat in a statement, forcing EU leaders to remove text that had been in a draft version, according to several people involved in discussions.

The watered-down language suggests the EU has some distance to go before it can start increasing pressure on Russia over the Syria conflict. Still, the German and French leaders warned after the meeting that if a current Russian-led cease-fire breaks down, sanctions could follow.

“Should Russia continue with these airstrikes, Russia would be exposed to sanctions,” said French President François Hollande in the early hours of Friday.