At the interbank foreign exchange market the rupee opened at 95.52, then lost ground and touched 95.56 in initial trade, registering a fall of 15 paise from its previous close.
The worst fighting between Washington and Tehran since the April 8 ceasefire has cast doubt on Trump's earlier claim that negotiations were close to ending the West Asia conflict.
Trump has repeatedly said that a peace agreement with Tehran is imminent, but diplomacy has stalled and the two sides have traded fire despite a ceasefire in place since April 8.