President Joko "Jokowi" Widodo demanded an apology for hurt national pride but also cautioned against exaggerating the incident with his neighbour.
Indonesia's flag has a red stripe above a white stripe, but it was inverted, making it look instead like the flag of Poland.
Malaysia apologised to Indonesia on Sunday for an "unintentional" mistake in printing the Indonesian flag upside down in a souvenir guidebook for the South-East Asian Games.
In the statement, Aman emphasized that "all measures have been taken to address this unfortunate situation" and reassured that "Malaysia places importance to its close and deeply rooted fraternal relations with Indonesia".
Mr Jamaluddin, who quickly issued the first apology late Saturday on Twitter, said the guidebooks will be corrected and reprinted.
"This is a very grave mistake and on behalf of the hosts, I apologise to Bapak Imam and all Indonesians over this very serious error", Khairy told a media conference after the 20-minute meeting.
"Friendship is the greatest legacy in sports, but a mistake in presenting a national identity is not justified", he said.
Mr Nahrawi, who earlier described the error as "very painful", said he accepted the apology.
Ties between Malaysia and Indonesia are generally cordial, but occasional perceived slights or when cases of an Indonesian maid being abused by a Malaysian employer come to light, passions in the republic flare up. This led to anger in Indonesia and "shameonyoumalaysia" started trending on Twitter.
"We hope these mistakes don't get repeated because flags are important symbols for each country and should be respected", he said.
The 27 websites now show photos of the upside-down Indonesian flag as appeared in the commemorative magazine of the regional sporting event, with a message underneath them that translates to, "Our nation's flag is not a plaything".