Black smoke billowed across the Jeddah circuit as seven-time world champion Lewis Hamilton and his fellow drivers took part in the first action of the weekend.
World champion Max Verstappen reported to his Red Bull team over the radio that he could detect the smoke.
"I smell a bit of a burning feeling," he said. "I am not sure if it is my car, or another car."
The al-Masirah satellite news channel run by Yemen's Houthi rebels claimed they had attacked an Aramco facility in Jeddah. The same fuel depot, 12 miles to the east of the track, was attacked on Sunday.
Second practice did not start until 8.15pm (5.15pm UK) following a short delay as the drivers and team principals were called by F1 boss Stefano Domenicali for a crisis summit.
A second meeting was staged deep into Friday night, with Domenicali emerging at 10:40pm local time.
"We have received total assurance that the country's safety is first," he said. "No matter the situation, safety has to be guaranteed.
"They have in place the systems to protect this area, the city and the places where we are going. We feel confident to trust the local authorities in that respect and, therefore, we will go ahead with the event."
Domenicali said the grid's 10 teams were in agreement that the race should not be cancelled.
"We are here all together," he continued. "We are standing together. We need to trust the local authorities, not only here but all around the world.
"If that's not the case then we would be in a situation that is not manageable."
Britain's former F1 world champion Damon Hill expressed his concern about the decision to press on with the race weekend, however, tweeting: "How incongruous is this? Nothing to be alarmed about. Race on. Will be interesting to see how this is dealt with. F1 literally playing with fire."
The drivers' scheduled media commitments were cancelled on Friday night and Hamilton's Mercedes boss Toto Wolff intimated that not all the drivers felt the race should still be staged. When asked if it was a unanimous agreement, he tellingly replied: "Between the team principals, yes."
FIA president Mohammed Ben Sulayem added: "We had meetings with high-level security, meetings with the team principals and with the drivers to assure them.
"They are targeting the infrastructure, not the civilians, and, of course, not the track.
"We've checked the facts and we've got assurances from the highest level that this is a secure place, the whole thing will be secure. Let's go on racing."
A statement from the Saudi Motorsport Company read: "We are aware of the attack on the Aramco distribution station in Jeddah earlier this afternoon and remain in contact with the Saudi security authorities, as well as F1 and the FIA to ensure all necessary security and safety measures continue to be implemented to guarantee the safety of all visitors to the Formula One Saudi Arabian Grand Prix as well as the drivers, teams and stakeholders.
"The race weekend scheduled will continue as planned. The safety and security of all our guests continues to be our main priority and we look forward to welcoming fans for a weekend of premium racing and entertainments."
An F1 spokesperson added: "Formula One has been in close contact with the relevant authorities following the situation that took place today.
"The authorities have confirmed that the event can continue as planned and we will remain in close contact with them and all the teams and closely monitor the situation."
Ferrari driver Charles Leclerc finished both practice sessions ahead of Verstappen. Hamilton was ninth and then improved to fifth later in the day.
Earlier, Hamilton reiterated his stance that he feels uncomfortable racing in Saudi Arabia.
Human rights' group, Reprieve, said a further 16 people have been killed since the mass execution of 81 men on March 12.
The United Nations' High Commissioner for Human Rights, claimed more than half of the 81 were killed for taking part in pro-democracy protests.
Speaking ahead of last year's race, Hamilton said: "Do I feel comfortable here? I wouldn't say I do."
And on Friday, the 37-year-old added: "My position is still the same as last year. It is obviously mind-blowing to hear the stories.
"I have heard there is a letter that has been sent to me from a 14-year-old who is on death row here. At 14, you don't know what the hell you are doing in life.
"We don't decide where we go to race in Formula One, but while it is not necessarily our responsibility, we are duty-bound to try and do what we can.
"It is important we try to educate ourselves, and with a little bit of difference, we can try to make sure we are doing something.
"But ultimately, it is the responsibility of those who are in power to really make the changes and we are not really seeing enough. We need to see more."
F1 has agreed a lucrative 15-year deal to race in Saudi Arabia, with the venue set to move from Jeddah to a purpose-built venue in Qiddiya, 25 miles outside of capital Riyadh, in the coming seasons.