The stuttering Saudis are midway through the final qualifying stage but find themselves second from bottom in the five-team Group B on four points from four games, with only the top two finishers guaranteed a place in the South Africa finals.
"My players have the ability, the quality and technical capability to get to the World Cup, I have no doubt about this," the Portuguese coach told Reuters.
"It has not been good so far, it will be difficult but we have to believe we can do this. I have to get this into the heads of my players, I have to make them believe.
"If they want it, they can have it, it's simple."
He accepts that the Saudis may have to rely on playoffs to reach South Africa 2010, with leaders South Korea and regional powerhouse Iran likely to grab the automatic berths.
The two third-placed sides from the Asian groups will contest a playoff, with the winner taking on Oceania champions New Zealand for the last remaining place at the 32-team finals.
Failure to reach the World Cup would be a tragedy in a nation where passion for soccer is as deep as the pockets of the oil-rich Sheikhs who run the Saudi game.
BIG CHALLENGE
"We've been there at the last four World Cups, it shows we have the quality and the ability to win when it's important," said Peseiro, who was assistant coach to Carlos Quieroz at Real Madrid from 2003-2004.
"We have a big challenge and we have some big changes to make with little time. I have to evaluate the tactics and the preparation. We have a lot of hard work to do."
His job, however, has not been made easy by injuries to some of his top players, including 2007 Asian player of the year and prolific marksman, Yasser "the sniper" al-Qahtani.
"I don't want to speak about this, or how my best players are injured," he said. "I have to focus on the players I have and making them perform, that's it."
The prospect of facing the axe should his team continue to underperform is also of no to concern him.
Anyone willing to work for a team that had changed its coach on average every eight months had to be prepared to be shown the door, Peseiro said.
"This is totally normal in the Middle East," he added. "It's not like Europe. They change coaches all the time here.
"I'm prepared for this. I'm not thinking about when I will leave. I'm thinking about one thing -- the World Cup.
"At this moment, all my time is focused on this and I will use all my commitment and all my dedication to make sure this (qualification) happens."
