Al-Assad was speaking on Sunday to Russia's Rossiya state television before this week's release of a UN report on the progress of the investigation into the assassination of former prime minister Rafiq al-Hariri.
He again declared Syria's innocence in the murder, and said the UN probe was politicised.
"The Middle East is the heart of the world, and Syria is the heart of the Middle East," al-Assad said. "If the situation in Syria and Iraq isn't good, the whole region will become unstable, and the entire world will pay for that."
An interim report by UN investigator Detlev Mehlis issued in October implicated top Syrian and Lebanese security officials in al-Hariri's assassination. The UN Security Council has warned Syria it has to cooperate fully with Mehlis' inquiry or face further action, a diplomatic code for sanctions.
Mehlis is to deliver the next report to the UN Security Council this week.
Government figures questioned
The names of top Syrian officials - al-Assad's brother, Maher, and brother-in-law, Assef Shawkat - were removed from the previous report in what was seen then as a UN attempt to soften the findings.
"If the situation in Syria and Iraq isn't good, the whole region will become unstable, and the entire world will pay for that"
Asked whether he would be eager to turn his relatives over to justice if they are named by investigators, al-Assad said that any citizen found guilty of involvement in the murder would be considered a traitor and severely punished, but added that the commission must provide hard proof for any of its claims.
"It's not names that matter ... but proof," al-Assad said. "We don't accept politicising the probe. There is a certain political situation around the commission that disorganises its work."
Russia has opposed sanctions against its Soviet-era ally, Syria, but strongly urged Damascus to cooperate with the UN investigators.
Despite the US and French pressure, "we have friendly relations with other countries which know and understand our position and realise that Syria is right," al-Assad said in the interview.