The former Ecuador coach wants his adopted nation to get behind the side as they look to reach the knockout round after the failure to progress past their group in 2000 and 2008
With matches against group favourites Spain and Japan looming, the opening fixture is a key opportunity for the Hondurans in their quest to qualify for the quarter-finals for the first time.
"We participated in Sydney and Beijing and now here," Suarez told reporters. "I don't want to make the first round, I want to continue in the Olympic Games.
"We played two rounds of qualifying to get here, but I believe that we can go further."
Suarez went on to describe the excitement of having secured qualification for the Games and recognised the size of the task ahead.
"It's a big privilege for us," he admitted. "We are honoured to be in this group and we think we have brought a worthy team for the first game.
"It is a deep group, which is so hard, but we will try each game to win."
The former Ecuador coach had decided on most of his starting line-up, but is unsure as to who will start with one-time Rangers target Jerry Bengtson in attack.
"I have doubts about the partner for Jerry Bengtson," he revealed. "Maybe today or tomorrow I will take the decision to play with Antony Lozano or Eddie Hernandez or the midfielder Mario Martinez."
The 52-year-old concluded by asking Honduras to get behind their country during the Games.
"Honduras believes sometimes if we have a mission," he added. "This is our mission, but the most important thing is the focus.
"In the pre-qualification no-one believed in us and we qualified for the Olympic Games. I hope that the people will remember this group for their strength and their heart after the end of the tournament."