Saudi border guards have opened fire on an Iranian fishing boat in the Gulf, killing a fisherman, Iran's Tasnim news agency said on Saturday, amid high tension between the two rival states.

"Two Iranian boats that were fishing in the waters of the Persian Gulf were pushed off their course by waves. There was shooting by Saudi border guards ... and one Iranian fisherman was killed," the semi-official agency quoted an Interior Ministry official as saying.

"We are pursuing this matter to determine if the Iranian boats had crossed the Saudi border or not, but the action of the Saudis does not comply with humanitarian and navigational principles," Majid Aqababai, director general of the ministry's border affairs, was quoted by Tasnim as saying.

There was no immediate Saudi reaction. Iranian reports said the incident happened late on Friday.

Relations between the two countries are at their worst in years. Last week Riyadh, along with other Arab governments, severed ties with Qatar, citing its support of Iran as a reason.

Days later, suicide bombings and shootings in Tehran killed 17 people. Shi'ite Muslim Iran repeated accusations that Saudi Arabia funds Sunni Islamist militants, including Islamic State. Riyadh has denied involvement in the attacks.

Iran and Saudi Arabia accuse each other of subverting regional security and support opposite sides in conflicts in Syria, Yemen and Iraq.