"An investigation is still being conducted on possible warning signs from Israel," van Weel said in his letter late on Friday evening.
At least five people were injured during the assaults on Thursday night and treated in hospital.
All were released later on Friday.
The incident concerned fans of the visiting Maccabi Tel Aviv team.
Police on Saturday said four people remained in custody of the 63 people initially detained.
"The Public Prosecution Service has stated that it aims to apply fast-track justice as much as possible," van Weel said, adding that it is "the absolute priority" to identify every suspect.
He said the investigation would also examine whether the assaults were organised, with an anti-Semitic motive.
Political leaders have already denounced the attacks as anti-Semitic.
Dutch Prime Minister Dick Schoof said on Friday he was "horrified by the anti-Semitic attacks on Israeli citizens" and had assured Israeli Prime Minister Benjamin Netanyahu by phone that "the perpetrators will be identified and prosecuted".
Schoof said on Saturday he would not attend the COP 29 meeting in Azerbaijan following the assaults in Amsterdam.
"I will not be going to Azerbaijan next week for the UN Climate Conference COP29. Due to the major social impact of the events of last Thursday night in Amsterdam, I will remain in the Netherlands", he said, adding Climate Minister Sophie Hermans was still going and that he would be replaced by a climate envoy.
Israeli fans were leaving the Dutch capital Amsterdam on special flights on Saturday.
Israeli authorities organised four flights for Saturday, when they would usually adhere to the Jewish Sabbath and take a day of rest, the ANP reported citing the Israeli embassy in The Hague.
It said a total of about 3000 football supporters had already departed from Amsterdam's Schiphol Airport and that further flights were planned for Sunday.
Videos on social media on what happened on Thursday showed riot police in action, with some attackers shouting anti-Israeli slurs.
Footage also showed Maccabi Tel Aviv supporters chanting anti-Arab slogans before Thursday evening's match.
Amsterdam banned demonstrations through the weekend and gave police emergency stop-and-search powers in response to the unrest.
Anti-Semitic incidents have surged in the Netherlands since Israel launched its assault on the Palestinian enclave of the Gaza Strip after the attacks on Israel by Hamas militants in October last year, with many Jewish organisations and schools reporting threats and hate mail.
with DPA
