Saudi Arabia has invited the Iranian foreign minister to Riyadh for the first senior meeting between the regional heavyweights since the start of the Arab Awakenings in which the two countries have engaged in a proxy war for influence.

The Saudi foreign minister, Saud al-Faisal, contacted his counterpart in Tehran on Tuesday after months of lower level communications between the countries, aiming to bring an end to a series of regional crises in which both are invested, principally in Syria.

"Iran is a neighbour, we have relations with them and we will negotiate with them," the minister said.

"We will talk with them in the hope that, if there are any differences, they will be settled to the satisfaction of both countries. Our hope is that Iran becomes part of the effort to make the region as safe and as prosperous as possible, and not part of the problem of the insecurity of the region."

The US has been attempting to persuade Riyadh to reach an accommodation with Iran, despite deep distrust between the two powers.

The US defence secretary, Chuck Hagel, will travel to the Saudi capital later this month in a bid to establish a detente, built on remarks earlier this year by the Iranian president, Hassan Rouhani, who suggested he wanted to improve ties.

Riyadh's invitation follows clear signs on the ground that a number of stand-offs in the region are slowly being doused through mutual consent. After 10 months of political paralysis, a new government was formed two months ago in Lebanon, where Saudi and Iran are key players in the fragile state's political fabric.

Political rhetoric has also cooled sharply in Bahrain, a bone of contention between the two countries well before the uprising of 2011, which pitched a large Shia majority against the Saudi-backed Sunni kingdom.

However, Syria remains a serious sticking point. The UN's Syria envoy, Lakhdar Brahimi, announced his widely anticipated resignation from his position on Tuesday.

More than three years into the war, Riyadh remains committed to seeing the end of Bashar al-Assad as president. Tehran is just as committed in ensuring the Syrian leader, or at least the systems and structures of his regime, remain in power, allowing it to continue project its influence from Tehran, through Baghdad, Damascus and southern Lebanon, where Hezbollah remains a key tool of Iranian foreign policy.

Both countries have invested heavily in arming and funding the opposing forces in Syria's war: Iran has been Assad's principal benefactor, directly supporting Hezbollah and an 11,000-strong Iraqi militia, as well as sending ammunition and money to Syrian forces. Saudi Arabia has supported rebel groups in southern Syria and near the Turkish border, where one of the two main factions, the Syrian Revolutionary Front, is a key beneficiary.

Despite their involvement, and Iranian officials' claims this week to the Guardian that Assad has won the war, there remains little chance that either side could win outright. Mutually assured destruction seems a most likely outcome, despite gains by Assad's regime and its backers, who are now in control of the country's third city Homs.

Saudi leaders are known to be wary of a US strategy in the region to bring Iran to the negotiating table where it would play a lead role in thrashing out a solution to Syria and other woes, with the probably exception of the Israeli/Palestinian conflict.

US president Barack Obama has anchored his regional foreign policy legacy in bringing Iran in from the cold, by first tempting it with a deal that would mean global legitimacy and an end to crippling economic sanctions in return for comprehensive concessions on its nuclear programme.

Saudi, along with Israel remain highly sceptical about claims that Tehran is prepared to change the capacity and direction of its nuclear programme, which has been active for at least 12 years, and which they and the US suspect is being used to produce a covert weapons capability.

• This article was amended on 14 May 2014. An earlier version referred to an Iranian majority when a Shia majority was meant.