Test player Shanthakumaran Sreesanth and fellow bowlers Ankeet Chavan and Ajit Chandila were all arrested Thursday, Indian police said, with 11 bookmakers also detained in connection with the inquiry.
The three cricketers play for the Rajasthan Royals in the Indian Premier League, as does former Test star Tait.
Tait's name was circulated in social media, on radio and a number of websites along with the three Indians, but he robustly denied any wrongdoing in a statement.
"I'm bewildered, I'm angry and I'm upset at the false suggestions I've been involved in any wrongdoing," he said in the statement.
"While I welcome the recent statements from police clearing me of any involvement, for a few hours I was deeply distressed by the rumours that were rapidly circulating about me, most of which were aired in the social media space.
"Not only were they without foundation, they highlight the danger of a medium that deals with innuendo rather than fact, the result of which has brought my name into question," he added.
"At no stage in my career have I engaged in spot or match fixing and I'm in discussions with my manager and legal representatives to examine how this episode unfolded and any further action I may take."
Cricket Australia said the head of its anti-corruption unit Sean Carroll had spoken to Tait following Delhi police's statement.
"Shaun reiterated to CA that he had absolutely no involvement in any of the issues that are currently being investigated," CA said in a statement Friday.
"CA is comfortable that Shaun is being appropriately supported in India and reminds those who have been speculating on the ongoing investigations to base their comments on known facts, not unsubstantiated rumour."
Spot-fixing is an illegal activity where a specific part of a game, but not the outcome, is fixed.
Sreesanth, who has played 27 Tests for India, is alleged to have been paid four million rupees ($75,000) to give away around 14 runs in an over while playing for the Royals against the Kings XI Punjab on May 9.
Chavan also allegedly agreed to give away the same number of runs in a match on Wednesday night against the Mumbai Indians in exchange for six million rupees ($110,000), police said.
A third player, Chandila, is accused of accepting two million rupees ($36,000), for giving away a set number of runs in a match between the Rajasthan Royals and the Pune Warriors.