BRUSSELS—Britain, France and Germany took a first step toward reimposing international sanctions on Iran, seeking to pressure Tehran into returning to compliance with the 2015 pact that has limited the country’s nuclear activities.

Tuesday’s move by the European powers, which say they remain committed to the 2015 nuclear deal and are seeking to save it, is their first significant response to Tehran’s gradual escalation of its nuclear program in recent months.

The three European countries, which are parties to the 2015 deal, triggered a dispute-settlement mechanism written into the agreement. That mechanism could result in the United Nations Security Council reimposing international sanctions on Iran’s economy, banks and some top officials within two months.

However, the Europeans can put that process on hold at various points, meaning that discussions over possible sanctions could stretch on for months.

Iran rebuked the countries on Tuesday for their decision, saying any misuse of the dispute mechanism would be met with a “serious and strong response.”