The new hopefuls bring the total number of candidates to six, though Assad has not yet announced his candidacy.
The opposition in exile and the West have said the election will be a "parody" of democracy, but the Syrian government says it aims to hold a "free and transparent" vote.
Assad, whose family has controlled the country for four decades, is expected to stand, despite more than three years of war that have claimed an estimated 150,000 lives.
Parliament speaker Mohammad al-Lahham said during a live broadcast that Sawsan Haddad, Samir Maala, Mohammed Firas Rajjuh and Abdel-Salam Salameh have now put their names forward to contest the post.
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They join a businessman, Hassan Abdullah al-Nuri, who studied in the United States, and independent MP and former communist Maher al-Hajjar as candidates.
Haddad, the only female candidate so far, was born in 1963 and is a mechanical engineer from Latakia province in the northwest, Assad's Alawite heartland.
Rajjuh was born in Damascus in 1966 and Salameh, born in 1971, is from central Homs province.
The candidates are all largely unknown, with few details immediately available about their backgrounds or political leanings.
New election rules prevent anyone who has lived outside Syria in the past decade from running, effectively preventing the opposition-in-exile from taking part in the vote.
Assad told AFP in January there were strong chances he would stand, and there is no doubt that he will win if he does.
Would-be presidential candidates must win the support of at least 35 of Syria's 250 MPs to do so.
The election will be Syria's first multi-candidate presidential vote, after a constitutional amendment did away with the old referendum system.