It said the decision was taken "bowing to public sentiments".
"Government has withdrawn the order. We have done this bowing to public sentiments," Goa Sports Minister Ramesh Tawadkar said hours after the legislators made public their decision to foot the bill for the trip themselves.
Five members of the group have, however, been allowed to visit the South American nation in their private capacity and the government will not sponsor the trip.
"Since government has cancelled the trip, I will no more be heading the delegation. That's why I have decided to opt out of it, I will not be going," he said.
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Tawadkar said the hype over the delegation's visit over the last two days had forced the ministry to cancel it.
Opposition Congress, which had earlier in the day refused to give credence to the MLAs announcement about picking up the tab for the visit themselves, however, insisted the government make public the noting on the file that the trip stood cancelled.
He said the government went into damage control after "the whole Brazil fiasco blew up in its face".
"This is just a damage control considering that Prime Minister Narendra Modi would be in the state tomorrow," he said.