* Energy projects focal point of agreement

* Saudis could invest in 'Made in Italy' fund

* PM has sought closer ties with Gulf countries

MILAN, Sept 4 (Reuters) - Italy and Saudi Arabia are in talks about a potential Saudi investment in Rome's new strategic fund, Italy's Industry Minister Adolfo Urso said on Monday, as the two signed a deal to forge closer economic relations, particularly in energy.

The "Made in Italy" fund, which was approved in May, will have an initial endowment of 700 million euros ($756 million) in 2023 and an additional 300 million next year in state cash.

Sources have previously told Reuters that Italy's Prime Minister Giorgia Meloni is courting sovereign wealth funds to increase the fund's firepower. The scheme would support Italian companies operating in key supply chains, while also aiming to boost procurement and reuse of "critical raw materials".

The fund would help support Italian manufacturing and make the country less reliant on external suppliers, but Meloni's coalition government is battling to contain a budget deficit.

Meloni has pursued tighter ties with Gulf countries since taking office last October, shrugging off the human rights concerns of previous governments.

Rome and Riyadh said on Monday they had signed an agreement to strengthen economic ties and boost investments in areas of strategic importance such as energy, where possible M&A deals were discussed, Urso told reporters in Milan.

"We have to start from the premise that the world is very different from the values to which we remain firmly committed," Urso said at an investment event.

Saudi Arabia will focus on energy, sustainability, supply chains and sport to expand its presence in Italy, Investment Minister Khalid al-Falih said at the same event.

The Kingdom, which has invested in sports such as soccer in other countries, already hosts the Italian Super Cup event, but has no direct investment in a major soccer club in Italy.

ENERGY HUB

Under Meloni, Italy sees itself playing an increasing role in linking the European Union with energy suppliers in the Middle East and North Africa as the EU cuts its with Russia.

The Memorandum of Understanding (MoU) with Saudi, seen by Reuters, lasts two years and will automatically be renewed for a further 24 months unless one of the parties notifies the other of its intention to quit six months before the expiry date.

Italian exports to Saudi Arabia totalled just over 4 billion euros in 2022, much from manufacturing, while imports totalled more than 7.4 billion euros, the bulk from oil products.

Also at the Milan event, leading Italian energy company Eni and Saudi Acwa Power agreed to jointly develop a green hydrogen project in the Middle East and Africa.

Acwa Power also struck a separate MoU with regional utility A2A and electrodes maker De Nora to cooperate on green hydrogen.

Saudi Arabia has a well advanced project dubbed NEOM to produce green hydrogen at home while Italy so far has not developed yet any plan to produce it in significant quantity. ($1 = 0.9267 euros) (Additional reporting by Giuseppe Fonte in Rome; Writing by Keith Weir; Editing by Angus MacSwan and Alexander Smith)