Formula One's governing body said last Friday that the race would be going ahead, despite calls from activists for it to be cancelled due to continuing unrest with regular clashes between police and anti-government protesters.
Three teenagers were wounded later that day at a rally in Manama after the funeral of a man shot during a protest two weeks ago.
Petrol bombs were thrown at police, who used tear gas. More demonstrations have been called for this week leading up to the Grand Prix, the biggest sporting event in Bahrain and one broadcast to a global television audience of many millions.
Last year's race had to be cancelled due to the February uprising and Formula One, whose teams have been deeply uneasy about going to Bahrain but have binding contracts to do so, has not returned since March 2010.
"You have some stuff going on in villages, but it's nothing that can't be handled," said Al Zayani. "I have no doubt at all that Formula One is not a target, not the teams, not the media."
Some drivers flew in on Monday, although others were spending time relaxing in nearby Dubai or Abu Dhabi. Advance personnel from Formula One Management have been in Manama for some days already.
Some freight is already in Bahrain while the cars should arrive at the circuit on Tuesday. Practice for the fourth race of the season starts on Friday and Formula One supremo Bernie Ecclestone has said he will be at the track.
Al Zayani said it was safe to go racing, even if there were some demonstrations across the tiny island.
"I think they (the protesters) will probably look out for the media to try and get their message abroad, which is fine. Let them express their opinion," he said.
The race is important financially for Bahrain, with organisers saying it brings in some half a billion dollars in spending.
"The country has gone through a tough year, we are still wounded in some aspects or another and we are on the way to regaining our health, so to speak. I think the race will be positive to the country," Al Zayani said.
"We need it as a country, we deserve it. I think we have passed the worst of the incidents and we need help to restore the country back on track."
Last year's bloody crackdown on protesters left more than 30 dead and has been condemned by international human rights groups while the decision to race has divided opinion.
Within Formula One, some television broadcasters have decided not to go while a member of the Williams catering staff has left the team by mutual agreement after she refused to travel on ethical grounds.
Much of the world media, particularly in Britain where a majority of the teams are based, has been opposed to the race going ahead.
Al Zayani suggested some of the other countries on the calendar had worse human rights records and questioned the motivation of some of the critics.
"I think every time we plug a hole about Bahrain, something else seems to pop up," he said. "I sometimes wonder and ask myself what is it that they've got against Bahrain? Are they just trying to find anything to spoil the race?"
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