Registrar of the Supreme Court said the five-judge bench would give their decision to the president and speaker of parliament within 24 hours, with a vote in parliament then expected to take place next week.
On Monday, the cabinet approved a proposal to scrap the two-term limit for presidents, which would enable Rajapakse to strengthen his grip on power by standing again in November 2016.
The main opposition United National Party called for a referendum and accused the government of "bulldozing" constitutional amendments through parliament.
Six lawyers acting for opposition political parties and civic rights groups filed objections during the proceedings at the Supreme Court on Tuesday.
"The constitutional amendments do not reflect peoples' wishes," opposition UNP General Secretary Tissa Attanayake told reporters at a press conference.
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Rajapakse came to power in 2005 and won a second presidential term in January, propelled by the victory of government forces over the Tamil Tiger