"I have no reason to believe that the Lebanese authorities won't co-operate with us fully," he said.
"They will not be held indefinitely and they will get their day in court."
The four detained generals were commanders of Lebanon's pro-Syrian security apparatus when al-Hariri was killed on a seaside street in Beirut, the Lebanese capital, on February 14, 2005.
Daoud Kheirallah, professor of law at Georgetown University, said that the UN investigation had, since its inception, suffered from charges that it had been politicised.
"The first UN investigator, Detlev Mehlis, has violated major issues of proper investigation, such as confidentiality, and all this has cast a huge cloud over the tribunal. There are people who suspect the tribunal may be a political arm of those who created it," he told Al Jazeera.
"This makes it compelling for all those who are involved, whether at the prosecution level or the trial level, to be totally independent and competent, with justice as the only objective."
A number of Lebanese politicians, including Saad al-Hariri, Rafiq's son, have accused Syria of being behind the bombing.
Al-Hariri broke with Syria and openly opposed Damascus' military involvement in Lebanon months before his assassination.
Syria denies any link to al-Hariri's death and has ended its 29-year military presence in Lebanon following international outcry at the bombing.
Trials could further antagonise current relations between pro- and anti-Syrian political entities in Lebanon.
The opening of the court does not mean that legal proceedings will be initiated immediately and investigations will continue.
A mixed Lebanese-international special tribunal had to be established by the UN Security Council after Lebanon's parliament was too divided to approve a hearing.
Administrators have said that the tribunal will take up to five years to be completed.
However, many people in Lebanon do not believe that any convictions will be made, despite reassurances from Bellemare.
"We will not be deterred by the obstacles or the size of the challenges,'' Bellemare said.
"We will go wherever the evidence leads us. We will leave no stone unturned."
Al-Hariri, a billionaire businessman, helped to rebuild downtown Beirut after the country's civil war from 1975-90.
Since his death Lebanon has suffered continuous political turmoil, with a Western-backed government at loggerheads with pro-Syrian opposition groups.