The ruling AK Party, whose roots lie in political Islam, says the reforms are needed to bring Turkey closer to EU democratic norms.
Opponents say they are an attempt by the AK Party to expand its grip on state institutions and undermine Turkey's secular principles. The AK Party denies the charges.
Parliamentary voting, which started on April 19, is set to finish by the end of this week, possibly on Thursday.
Prime Minister Tayyip Erdogan rallied his deputies in a speech in parliament ahead of the start of Sunday's session, calling for solidarity against opposition challenges.
"We face a difficult marathon this week due to the second round of discussions on constitutional changes. We in the AK Party will continue the process in the second round...with the same solidarity, sacrifice, seriousness and courtesy," he said.
"It appears that the constitutional changes will go to a referendum and our dear people will say the last word on this subject after parliament," he said.
Investors are following the process closely, fearing it could increase tensions and lead to an early general election, due in July 2011. The main opposition party has said it would appeal to the country's top court to annul the amendments.
Erdogan's party has 335 seats in the 550-seat parliament, but needs 367 votes to pass the reforms outright. It failed to achieve sufficient support to do so in the first round.
FEARS OF COURT CHALLENGE
Erdogan has already said he will call a referendum if opposition parties fail to back the reforms.
Under law, the government can do so if it wins at least 330 votes, which it did in the first round of voting.
Political commentator Mehmet Ali Birand said the nightmare for the AK Party would be the failure to secure the sufficient votes in the second round. The prospect of a court challenge was also clouding the horizon.
"Against this backdrop we can say that the clouds are increasingly darkening and the weather worsening over Ankara," he said in a column in Posta newspaper.
One of the key reforms in the package would make it harder to ban political parties. Almost 20 parties have been closed down since the current constitution was introduced in the wake of a 1980 military coup.
The AK Party itself narrowly survived a court attempt to ban it in 2008 for contravening the country's secular constitution.
The package also includes reform of the Supreme Board of Judges and Prosecutors (HSYK) and the Constitutional Court. Critics say the AK Party is pushing through these changes to boost its influence over the judiciary.
The government also wants to limit the power of military courts by allowing military personnel to be put on trial in civilian courts for crimes against the constitutional order.
Dozens of officers, including retired and serving generals, have been charged in civilian courts in recent months in connection with alleged plots to overthrow the government.
