BEIJING, July 10 (Reuters) - The mayor of Beijing has told the governor of Saudi Arabia's sovereign wealth fund he hoped the fund would further expand its business in the Chinese capital, state media said on Wednesday.

Beijing's diplomatic push to court U.S. ally Saudi Arabia comes amid its frustration over what it sees as Washington's weaponisation of economic policies, nudging it to expand ties with countries in Europe, the Middle East and Africa.

China offers many investment opportunities, the mayor, Yin Yong, told Yasir Al-Rumayyan, the chief of the Saudi Public Investment Fund, at a meeting on Tuesday, the official Beijing Daily newspaper said.

Yin said he hoped the fund would guide two-way investments by companies of both countries, deepening co-operation in areas such as industrial investment, green development, and energy transition.

Al-Rumayyan said he hoped to keep up close communication and exchanges with Beijing for co-operation on sustainable development and renewable energy, the paper added.

One of the world's largest sovereign wealth funds, the Saudi Public Investment Fund has a sprawling portfolio of investments, from date farms to multinational conglomerates.

China is seeing a surge in investment from funds in Gulf nations at a time when some Western financial firms are reining in investments in the country, deterred by concerns about its economic recovery and geopolitical risks.

Qatar's sovereign wealth fund has agreed to buy a 10% stake in China's second-largest mutual fund company, Reuters reported last month, citing sources. China also recently approved its first exchange-traded funds investing in Saudi Arabia equities.

While economic co-operation between Beijing and Riyadh remain anchored on energy interests, ties in trade, investment and security have been expanding. China is Saudi Arabia's top trading partner.

Saudi Arabia's ambitious Vision 2030 plan aims to diversify its economy away from fossil fuels to develop a vibrant private sector.

The government of the world's biggest oil exporter hopes its nascent manufacturing industry will one day turn out everything from computer chips to tyres, in a wider economic transformation. (Reporting by Bernard Orr and Beijing newsroom; Editing by Miral Fahmy and Clarence Fernandez)