While JASTA applies to any act of terrorism on US soil, the primary focus has been on Saudi Arabia over its alleged involvement in the 9/11 attacks.
In opposing the law, President Obama warned it would harm US interests by undermining the principle of sovereign immunity, opening up the US to private lawsuits over its military missions abroad.
The Saudi government has denied it had any ties to the terrorists who carried out the 9/11 attacks. In its statement on Thursday, it condemned the passed legislation, saying that the enactment of the law was a matter "of great concern."
"The erosion of sovereign immunity will have a negative impact on all nations, including the United States," the Saudi foreign ministry said in its statement on the same day.
"I’m afraid that this bill will have dire strategic implications for the United States," Salman al-Ansari, head of the Saudi American Public Relation Affairs Committee (SAPRAC), told AFP.
This partnership has helped provide US authorities with accurate intelligence information that helped prevent attacks, he said.
Riyadh and Washington have a decades-old relationship based on the exchange of American security for Saudi oil.
"Saudi has been stabbed in the back by this unthoughtful and unrealistic bill," Ansari said.
Meanwhile Russian politician Igor Morozov, member of the Committee for Foreign Affairs of the Council of the Federation, the Upper Chamber of the Russian parliament suggested that the cooling of relations between Saudi Arabia and the US could alter the balance of power in the Syrian conflict which, in turn, will result in serious political consequences for the whole Middle East region.
"A new turn in Saudi foreign policy will result in strengthening ties with players like Russia and China," the politician suggested in his interview with Russian online newspaper Gazeta.ru.
The politician noted that the Middle Eastern countries are in fact ready for dialogue with their ideological adversaries, citing as an example the evident thaw in relations between Iran and Turkey after the cooling of relations between Ankara and Washington.
The newspaper said that a number of experts it questioned on the issue also did not rule out a chance for a dialogue between Damascus and Riyadh regardless the enmity of the latter towards President Assad.
It also quotes one Russian source familiar with the situation in the Syrian high brass as saying that there are a number of Sunnis who could enter into dialogue with Saudi Arabia.
Dr. Theodore Karasik, the senior advisor at Gulf State Analytics, also suggested that Russia will undoubtedly use the discrepancies between the US and Saudi Arabia for its own purposes "directly on the ground."
However he further suggested that there is also a strong probability that the spat between Washington and Riyadh might result in the strengthening of the so-called "moderate opposition" in Syria by the Saudis, who previously adhered to the US urge not to supply them with arms.