Nine Turks died when Israeli naval commandos stormed the "Mavi Marmara," which was part of an aid flotilla to break a naval blockade of the Gaza Strip. One more died in the hospital in 2014.
Ties between Israel and Turkey crumbled after the raid, but in June they finally agreed to end the bitter six-year row after months-long secret talks.
Israel had offered an apology over the raid, permission for Turkish aid to reach Gaza through Israeli ports, and a payout of $20 million to the families of those killed.
Turkish officials confirmed the amount was transferred to the justice ministry account last month.
Under the deal, both sides agreed that individual Israeli citizens or those acting on behalf of the government would not be held liable.
Families of the victims however say they will press on with their legal battle until the alleged perpetrators are brought to justice.
Cigdem Topcuoglu, an academic from southern Adana province, said her husband was killed as the couple embarked on the ship.
"We are certainly not accepting the compensation," she told AFP in Istanbul. "They will come and kill your husband next to you and say 'take this money, keep your mouth shut and give up on the case'. Would you accept that?"
In total, there were six ships in the flotilla that were boarded in international waters about 130km from the Israeli coast.
Life sentences sought
After the deal with Israel, an Istanbul court on October 19 held another hearing in the trial of the four former Israeli military commanders, though it was later adjourned to December 2.
Turkish prosecutors are seeking life sentences for former military chief of staff Gabi Ashkenazi, former navy chief Eliezer Marom, former military intelligence head Amos Yadlin and former air force intelligence chief Avishai Levy, who went on trial in absentia in 2012.
"We have no intention to drop the lawsuits," Topcuoglu said.
Human rights lawyer Rodney Dixon said the criminal case against the accused must go on "at all costs".
"We are strongly supporting the case here in Turkey and our very firm plea to the court has been that they must continue with the case," he said.
"The so-called agreement between Israel and Turkey is not a treaty that is enforceable. It is unlawful under international law, under the convention on human rights and Turkish law."
Families say they were not informed of any details about the deal with Israel and they have not received any money.
Ismail Songur, whose father died in the raid, said: "Nobody from the Turkish government asked our opinion before they struck a deal. "Unfortunately the Turkish government is becoming a part of the lawlessness carried out by Israel."
"Even if families of the victims accept the money, that would not affect the case," said Gulden Sonmez, one of the lawyers in the trial and also a passenger on the ship.
"That is a criminal suit, not a suit for compensation. The $20 million is an ex gratia payment. It's a donation and cannot be accepted as compensation."
A vocal advocate of the Palestinian cause who regularly lambasts Israeli assaults in Gaza, Turkish President Recep Tayyip in June caught many by surprise when he criticised the 2010 aid mission to Gaza, only a few days after his government reached an accord with Israel.
"Did you ask then-prime minister to deliver humanitarian aid from Turkey?" he said in comments seen as veiled criticism of the Turkish Islamic charity IHH that organised the flotilla.
Bulent Yildirim, head of the IHH, said the legal case would never end. "Those who believe the case would drop will be disappointed."