But the court ruling, issued on Monday, was unlikely to have a "significant effect" on attempts to restore full diplomatic relations between Israel and Turkey, which were badly damaged by the raid, officials said.
"Of course we’re not happy about it. It seems more political than legal," said Defence Minister Moshe Yaalon during a tour of the Jordan Valley Tuesday, in remarks relayed by his office.
"We were ready to set things right with Turkey and regulate relations with them," he said.
"There is unfortunately no ripeness on the Turkish side to make things better, and this event is part of the campaign, which is being conducted for Turkish domestic political reasons, among others."
Israel and Turkey have been locked in more than a year of talks over compensation for the deaths of nine Turks in the deadly Israeli raid on a Gaza-bound flotilla in May 2010.
The number rose to 10 last week after the death one of the injured, who had been in a coma, a Turkish NGO said.
- 'Political pranks' -
The Istanbul court is to ask Interpol to alert police forces around the word to the arrest warrants, but Israeli foreign ministry sources told Maariv newspaper it was unlikely that the international police body would take the request seriously.
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"The danger that countries with which Turkey has extradition agreements will cooperate with this initiative does not appear tangible, because the Turks do not have evidence that meets the threshold conditions for extradition," one source told the paper.
"Interpol is a professional body that does not cooperate with political pranks," he said.
The court's move to obtain arrest warrants for the four men, who are being tried in absentia, "will not have a significant effect on the efforts being made in the two countries to reach a reconciliation agreement although the latest development in the trial will now serve as another factor that will delay its signing," he said.
The court ruling is part of an ongoing criminal trial of the four men on charges brought by Turkish NGO IHH and the victims' families in 2012.
On Monday, an Israeli official told AFP the court's decision was a "ridiculous provocation."
Talks on compensation began after Israel extended a formal apology to Turkey in a breakthrough personally brokered by US President Barack Obama. Earlier this year, senior officials in Ankara said a deal on compensation was "close."
Within the framework of the deal, Israel is reportedly prepared to offer $20 million (14.7 million euros) in compensation to the families of those killed and wounded in the raid.
In exchange, Turkey would drop all further legal claims.
The four Israeli officials named in the lawsuit are former chief-of-staff Gaby Ashkenazi, former navy chief Eliezer Marom, former military intelligence head Amos Yadlin and former air force intelligence chief Avishai Levy.