After chairing his first cabinet session since returning to Beirut in late November, Saad Hariri said in a statement that the government's "political components agreed to disassociate itself from any conflicts and wars and from internal affairs of Arab countries".
Hariri said he changed his mind about quitting after receiving assurances from other members of government that they would not meddle in foreign conflicts.
Some Lebanese officials have said that Riyadh forced Hariri to tender his resignation, although Saudi Arabia has denied this.
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Aoun had said he would not accept Hariri's resignation unless he presented it in person.
The resignation was seen as part of the boiling tensions between the Saudi kingdom - which had long backed Hariri - and its regional rival Iran.
Sources in the prime minister's office told Asharq al-Awsat that the new ministerial statement would focus on four main points, including dissociating Lebanon from Arab conflicts, preserving good relations with Arab countries, stopping harmful media campaigns and committing to the Taif Accord.
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Dastyari, who remains in Parliament, had previously said that a Chinese company with links to Beijing had paid a A$1,670 (US$1,275) travel bill for him.
The policy had already been adopted by Hariri's cabinet, formed in 2016 after a settlement across political divides that saw Michel Aoun appointed president and the creation of a government including Hezbollah deputies.
Lebanese Prime Minister Saad Hariri attends a cabinet meeting at the presidential palace of Baabda, east of the capital Beirut, on December 5, 2017.
He delivered his resignation announcement from Saudi Arabia and spent the next two weeks there amid rumours that Riyadh was holding him "hostage". The militant group plays a key role in Lebanon's government but its armed wing is fighting in Syria to support fellow Iran ally President Bashar al-Assad.
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