Heavily indebted Tunisia has secured a $1.9 billion loan while Egypt is close to finalising a deal.
Two rival opposition groups stage one of the biggest days of protest so far against President Kais Saied, denouncing his moves to consolidate political power as public anger grows over fuel and food shortages.
The vote is set for nearly a year and a half after President Kais Saied suspended the Ennahda-dominated assembly and sacked the government, later pushing through a constitution enshrining his rule.
Tunisia's President Kais Saied dismissed 57 judges on June 1, accusing them of corruption and protecting terrorists - charges that the Tunisian Judges' Association said were mostly politically motivated.
The low voter turnout revealed that President Kais will face a major challenge in turning the public sentiment in his favour.
The referendum saw just 27.5 percent of 9.3 million registered voters cast ballots, with an overwhelming 92-93 percent supporting the new constitution.
New constitution greatly expanding presidential powers is set to take effect following a referendum that an exit poll indicated was easily won by the "yes" side but with a very low turnout of just over 27%.
Voting runs from 6:00 am (0500 GMT) to 10:00 pm at some 11,000 polling stations across the North African country, while there is no clarity yet on when the results will be announced.
The constitutional referendum, which is expected to pass amid boycott calls, will concentrate all powers in the hands of the president.
Rached Ghannouchi, leader of Tunisia's biggest and most organised political party Ennahda, arrived for questioning by an investigating judge at an anti-terror centre as his supporters rallied outside the courthouse in the capital Tunis.
The amended draft makes changes to two articles, though it still retains a broad range of powers for the head of state.
Judge orders freeze on financial assets of ex-speaker of the African country's dissolved parliament Rached Ghannouchi, his son, ex-PM Hamadi Jebali, ex-FM Rafik Abdessalem and several other people.
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