Saudi officials deny prince Mohammed's involvement and say Khashoggi's death resulted from a "rogue" operation, but it severely marred his reputation as a potential reformer.
Biden now appears ready to re-engage with a country that has been a key strategic ally of the United States for decades, a major supplier of oil and an avid buyer of weapons.
Washington wants the world's largest exporter of crude to open the floodgates to bring down soaring gasoline prices, which threaten Democratic chances in November mid-term elections.
Biden was expected to meet with 86-year-old Saudi King Salman before participating in a "working session" headed by prince Mohammed, according to a programme distributed by Saudi officials.
US officials are also touting efforts to promote integration between Israel and Arab nations.
Saudi Arabia has refused to join the US-brokered Abraham Accords which in 2020 created ties between Israel and two of the kingdom's neighbours, the United Arab Emirates and Bahrain.
The kingdom has repeatedly said it would stick to the decades-old Arab League position of not establishing official ties with Israel until the conflict with the Palestinians is resolved.
But it is showing signs of greater openness towards Israel, and on Friday morning announced it was lifting overflight restrictions on aircraft travelling to and from Israel, a move Biden hailed as "historic".
Israeli caretaker prime minister Yair Lapid said the decision to scrap airspace restrictions was "only the first step" as the country seeks to strengthen regional ties.
On Saturday Biden is expected to meet Arab leaders from the six-member Gulf Cooperation Council as well as Egypt, Jordan and Iraq to discuss volatile oil prices and Washington's role in the region.
'Political horizon' in Bethlehem
Jeddah marks the final stop on Biden's Middle East tour, following Friday's talks with Palestinian president Mahmud Abbas and meetings with Israeli officials a day earlier.
With Palestinians banned by Israel from political activity in Jerusalem, the US president travelled to Bethlehem in the occupied West Bank to meet Abbas.
Standing alongside Abbas, Biden reiterated his commitment to a two-state solution to end the Israeli-Palestinian conflict and said there "must be a political horizon that the Palestinian people can actually see".
"I know that the goal of the two states seems so far away," he said in Bethlehem.
The Palestinian president said he was "taking steps" to improve relations with Washington and aimed to see the US consulate to Palestinians in Jerusalem reopen. The consulate was shuttered by Trump.
With Israeli-Palestinian peace negotiations moribund since 2014, the US delegation has been focusing on economic measures.
Biden made clear on Thursday he had no plans to reverse the controversial move by Trump to recognise Jerusalem as Israel's capital, which infuriated Palestinians who see its eastern sector as the seat of their future state.
'Justice for Shireen'
Biden was greeted in Bethlehem with a billboard reading "Justice for Shireen," referring to Shireen Abu Akleh, the veteran Palestinian-American journalist shot dead in May while covering an Israeli army raid in the West Bank.
The family requested to meet Biden during his visit, but his administration has instead invited the family to Washington.
"I think if President Biden (can) find an hour and a half to go and attend a sport activity, he should have respected the family and given them 10 minutes to listen to them," said Samer Sinijlawi, chairman of a Palestinian nonprofit, the Jerusalem Development Fund, after Biden on Thursday attended a ceremony for Jewish athletes.
Speaking alongside Abbas, Biden said the US "will continue to insist on a full and transparent accounting" of Abu Akleh's death.
Washington earlier this month concluded she was likely shot from an Israeli military position, but that there was no evidence of intent to kill.