Shaikh Mashouk al- Khaznawi, who went missing last month, was buried on Wednesday in his native Qamishli, northeastern Syria, where he used to lead prayers.
The funeral drew tens of thousands of mourners, according to Kurdish officials.
"Security forces arrested two members of the gang which carried out the crime of kidnapping and assassinating Shaikh al-Khaznawi," said the Tishrin government daily.
It named them as Yassin Matar Hindi, 43, a Damascus employee of the state electricity authority, and Mohammed Matar Abdullah, 36, prayer leader of a mosque in Hassakeh, northeast Syria.
The two are both natives of Deir Ezzor in the same region, it said.
Three other members of the gang are on the run, Tishrin said, giving their names as Ismail Kadri Malla, also from Hassakeh; Samir Tlaigeh from Aleppo, north of Damascus, and Said Haidaleh from Deir Ezzor.
Syrian Kurds want their cultural
and political rights recognised
On Wednesday, the Interior Ministry had said all five were arrested.
But Kurdish parties were unconvinced.
"The reports by the Syrian media are dubious; they conceal political motives," Hassan Saleh, secretary-general of the banned Kurdish party Yakiti, told reporters in Qamishli.
He called for a commission of inquiry, "to uncover the truth", and declared that sit-in protests would be held in Kurdish areas of northeast Syria as well as in Damascus and Aleppo.
"We know the criminals who killed our father. We are going to publish a communique about this," said Mohammed Murad Khaznawi, 30, one of the murdered sheikh's 16 sons.
"If we had been in Switzerland, I would have told you the truth but we are in Syria," he said.
In the town of Qamishli, shops kept their shutters down on Thursday in a sign of mourning. Inside a huge tent erected for the family to receive condolences, several mourners also insisted on finding out the truth of the murder.
Despite the official version, Amnesty International said al-Khaznawi was "at least the sixth Syrian Kurd to have died as a result of torture and ill-treatment since March 2004".
The 46-year-old religious leader "died on 30 May, 20 days after he 'disappeared', apparently detained by Syrian military intelligence at an unknown location", the rights group said.
It called for Syrian authorities to launch "an immediate, independent investigation" into the sheikh's death "in custody".
Just days before his disappearance, al-Khaznawi is reported to have called in an interview with the Canadian newspaper, the Globe and Mail, for regime change in Damascus.
"We know the criminals who killed our father. We are going to publish a communique about this"
Mohammed Murad Khaznawi,
Son of slain cleric Sheikh Mashouk al-Khaznawi
"Either the regime will change or the regime must go ... I could not have said this five years ago because the Americans weren't in (neighbouring) Iraq five years ago," he said.
His disappearance led some 10,000 Kurds to demonstrate in Qamishli on 21 May, demanding that the Syrian authorities release news of the cleric's whereabouts.
Qamishli was the site of riots in March 2004 that began with stadium fighting between Arab and Kurdish football fans and grew into bloody clashes between Kurdish protesters, Syrian security forces and Arab tribesmen.
Kurdish sources reported that 40 people died in the fighting. Syrian authorities said 25 were killed.
Syria is home to some 1.5 million Kurds, around nine percent of the population. They are demanding to have their language, culture and political rights recognised.