Assad, who is battling a three-year-old rebellion against his rule, has not said whether he will stand in the election due by July, but allies in Russia and Lebanon's Shi'ite movement Hezbollah have predicted he will stand and win.
International powers who back Syria's opposition have described the plans to hold elections as a "parody of democracy" that would destroy peace talks.
Syrian Information Minister Omran Zoabi nevertheless said elections would not be delayed and that military operations would continue regardless of the poll, pan-Arab daily Al-Hayat reported on its website on Tuesday.
"It is not for any authority to postpone or cancel this election, which will be run on schedule," the newspaper quoted him as saying.
"We will not allow security, military, or domestic or foreign political reasons to delay or cancel the presidential election."
Assad's forces have advanced around the capital Damascus and the Lebanese border in recent months, helping secure the country's centre under government control.
The president's allies have meanwhile voiced confidence as peace talks in Switzerland between the government and Western-backed opposition politicians in exile have collapsed.
On Monday, a former Russian prime minister was quoted as saying Assad forecast that much of the war's fighting would be over by the end of the year.
The same day, the leader of Hezbollah, which has sent fighters to Syria to aid Assad, was quoted as saying the president no longer faced a threat of being overthrown.
The Syrian war, which started as a peaceful protest movement, has killed over 150,000 people, forced millions more from their homes, and seen the government lose control over swathes of northern and eastern Syria to rebel fighters.
(Reporting by Alexander Dziadosz; Editing by Angus MacSwan)