Prince Mohammed kicked off his Arab tour on Thursday by visiting the United Arab Emirates.
Egyptian President Abdel Fattah al-Sisi underlined the strength of Cairo's ties with Riyadh and called Saudi Arabia's security and stability "an inseparable part of Egypt's national security".
The activist group's complaint also mentioned allegations that women's rights activists have been tortured by the Saudi government with electrocution and flogging, as well as the extrajudicial killing of Jamal Khashoggi.
"It was premeditated murder", he told the German newspaper, rather than a last resort after they failed to convince him to return to Saudi Arabia.
Other Republican senators, including Lindsey Graham, Rand Paul and Bob Corker, have been vocal about their belief of Saudi Arabia's Crown Prince's involvement in Khashoggi's killing.
Tunisian President Essebsi's office said Tunisia denounces the journalist's killing and wants a full investigation, but doesn't want it to be used to destabilize Saudi Arabia.
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In a historic move, the Crown Prince visited the Cathedral of St. Mark in Abbasia, where he met with Pope Tawadros II and church leaders.
The New York-based rights group said it had filed a submission with Argentine prosecutors calling on them to invoke the country's universal jurisdiction statute to prosecute the crown prince for alleged war crimes committed by the Saudi-led coalition in Yemen.
Prince Mohammed's current tour comes ahead of his participation in the G20 summit in Argentina, starting on Friday.
Tunisia is one of the few Arab states where demonstrations are allowed, following a 2011 uprising that toppled veteran ruler Zine el-Abidine Ben Ali and ushered in freedom of speech and the press.
Khashoggi has been missing since he entered the Saudi consulate in Istanbul on October 2.
"At the moment there is no reason not to meet with the crown prince", Cavusoglu said.
Argentina has not issued any official comment on HRW's request.
In its petition, HRW highlighted almost 90 "indiscriminate and disproportionate airstrikes on civilians" in which the USA -backed Saudi coalition has "hit homes, markets, hospitals, schools and mosques" across Yemen.