Unionist and nationalist politicians took part in an Armistice Day ceremony in Parliament Buildings on Wednesday.
The national anthem was sung at the end of the event, but had not been on the order of service agreed by the speaker.
Sinn Féin said the singing had been a "childish stunt" by some unionists.
Sammy Morrison, a press officer for the Traditional Unionist Voice, started the singing.
He said Sinn Féin should reconsider attending remembrance events if they had an issue with the singing of the national anthem.
Sinn Féin MLA Mitchel McLaughlin, the assembly speaker, led the service.
In a letter to MLAs on Friday, he said he recognised that anthems are part of the act of remembrance for many people, but for many others they are not.
His commitment to represent all MLAs was a serious one, he said, but that often meant making difficult judgements.
He added that his door is open for MLAs and others to speak to him about how Stormont can achieve the same outcome of wide attendance and inclusive participation "without some of the tensions which emerged between the parties" after this week's event.
The kind of approaches he will find useful will not be "just the easy solutions based on one perspective", he said, but will recognise that as speaker he must represent politicians with "different views and different allegiances".
A remembrance service at Stormont that ended in a row over the national anthem had been arranged to allow as many MLAs as possible to attend, the speaker of the Northern Ireland Assembly has said.