DUBAI - Iran said it was lifting visa requirements for 33 countries, including Gulf states like Saudi Arabia with which Tehran had frosty relations for years until a recent rapprochement, the Iranian Students News Agency said on Thursday.

"The ministry of tourism believes that an open-door policy will showcase Iran's determination to engage with different countries of the world," the semi-official ISNA reported.

The decision will increase to 45 the number of countries or territories whose citizens can visit Iran without needing to obtain a visa, it said.

The move is another step towards thawing relations between Iran and Saudi Arabia in particular after years of tension between the two oil-producing Gulf rivals.

Riyadh and Tehran have aligned themselves with warring parties in Syria, Iraq and Yemen in the past decade. Attacks on Saudi oil infrastructure, which Western officials blame on Iran and its Arab proxy forces, threatened in recent years to send the Middle East into further conflict. Iran denied involvement in those attacks.

Iran and Saudi agreed to restore full diplomatic relations, severed in 2016, under a Chinese-mediated agreement in March.

Nationals of Saudi Arabia, the United Arab Emirates and Qatar are included in the decision to waive visa requirements, in addition to Bahrain, with whom Tehran has not yet re-established full ties.

ISNA gave a full list of the countries, which included Lebanon, Tunisia, India, several Central Asian, African and "Muslim" nations. Only one Western-allied European nation was on the list, Croatia, a small member of the European Union and NATO.

"Russians will only profit from this visa exemption if they are visiting the country in groups," ISNA added.

Omani nationals had been able to travel to Iran visa-free prior to this announcement.

Iranian pilgrims will for the first time in eight years begin regular travel to Saudi Arabia from Dec. 19, Iranian media reported on Wednesday.

(Reporting by Elwely Elwelly and Dubai Newsroom; editing by Mark Heinrich)