Khashoggi, a Saudi journalist and columnist for The Washington Post, had gone missing since entering the Saudi Consulate in Istanbul on Oct. 2.
After days of denying to know his whereabouts, Saudi Arabia on Saturday claimed Khashoggi was killed during a fight inside the consulate.
In a statement, Egypt`s Foreign Ministry said it "values the results of preliminary [Saudi] investigations in the case."
"The decisions and actions taken by Saudi King Salman bin Abdulaziz are consistent with respect of the principles of law and application of justice," it added.
A similar praise came from the United Arab Emirates, which "hailed King Salman`s directives and decisions," according to the official news agency.
Bahrain said decisions by the Saudi monarch came "to establish justice and equity and uncover the facts," Saudi Arabia`s Al-Ekhbariya TV channel said on Twitter.
Palestine, for its part, said "Saudi Arabia, under the leadership of the Custodian of the Two Holy Mosques King Salman bin Abdulaziz and Crown Prince Mohammed bin Salman, will remain the state of justice, values and principles."
It hailed the Saudi decisions for ?establishing justice, fairness, facts and law," according to the official Palestinian news agency Wafa.
The Yemeni government said in a statement the findings of the Saudi probe "reflect the continuous and serious follow-up by the Saudi institutions," according to the official Saba news agency.
The statement said Riyadh "has always reviewed any mistake that may occur from one of its institutions and work to address it immediately and take the necessary actions and bring perpetrators to accountability as what happened in this incident [the killing of Khashoggi]."
Kuwait`s Foreign Ministry also welcomed the Saudi version of the events, saying it "reflects the Kingdom?s concern on respect of the principles of law".
Oman, for its part, described the Saudi measures regarding Khashoggi as "transparent."
In a statement, the Omani Foreign Ministry said it "welcomes all transparent measures taken by the Kingdom."
Jordan said the Saudi explanation was "necessary to clarify the circumstances of the case and bring those responsible to accountability."
Djibouti hailed the "interest" of the Saudi king to uncover the facts about Khashoggi`s killing, the official Saudi Press Agency reported.
The Cairo-based Arab League said the Saudi explanation "reflects a great concern to unveil the truth and take the necessary legal measures."
In a statement, it reiterated rejection of threats to impose economic sanctions or take unilateral measures against Saudi Arabia over the case.
The Organization of Islamic Cooperation (OIC) also welcomed "the crucial decisions that included the arrest of 18 suspects in this case following the preliminary investigations by the [Saudi] Attorney-General."
Abdullatif bin Rashid Al Zayani, the Secretary-General of the Gulf Cooperation Council, for his part, described the Saudi measures as "firm" and "reflected the commitment of the Kingdom`s leadership to clarify the facts to the world public opinion."
On the day of Khashoggi`s disappearance, 15 other Saudis, including several officials, arrived in Istanbul on two planes and visited the consulate while he was still inside, according to Turkish police sources. All of the identified individuals have since left Turkey.
A joint Turkish-Saudi team completed an investigation into the case on Thursday after searching the residence of the consul general as well as the Saudi Consulate in Istanbul.
Ediiting by Chaidar Abdullah