Despite the growing risk to Middle Eastern supplies, crude prices have been depressed by fears of an economic slowdown due to the US-China trade dispute.
The tanker explosion will spur fresh concern about potential conflict in the world's most important crude-producing region after attacks on ships and drones earlier this year, and most recently a strike on Saudi Arabian energy infrastructure.
The vessel, from Iran's national oil company (NOIC), was 60 miles (97km) from the Saudi port city of Jeddah when the incident took place, reports say.
The official also said that the missiles had possibly been launched from the direction of Saudi Arabia, but he did not offer any evidence for his assertion. The leak was later plugged, Iranian state television reported.
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Oil prices jumped above $60 a barrel in London after the attack.
Tension in the region has been high since the United States withdrew from an worldwide nuclear deal and reimposed sanctions on Iran.
Esper later told reporters that the deployments were in response "to continued threats in the region" and came after a conversation with bin Salman about "efforts to protect from further Iranian aggression".
Oil prices had eased after spiking above $70 in response to the September 14 attacks on Saudi oil sites, which shut down 5.7 million barrels per day (bpd) of production, about half of Saudi output and roughly 5% of global supply. While Yemen's Houthi rebels, who have an on-going war with the kingdom since 2015, claimed the attack, numerous officials and analysts pointed at Tehran.