The Board of Control for Cricket in India (BCCI) have confirmed that the team's tour of Australia will continue despite the on-going row between the two sides.
The BCCI took the decision to suspend the tour on Monday, having taken offence at the decision to ban Harbhajan Singh for three matches for racially abusing Andrew Symonds.
The Indians had also complained to the ICC about "incompetent" umpiring in the second Test in Sydney.
However, the BCCI have been appeased by the ICC's swift actions to assure the tour continues.
Firstly, the ICC decided to replace Bucknor with Billy Bowden for the third Test in Perth, while confirming a code of conduct commissioner to adjudicate on India's appeal against the decision to ban Harbhajan.
In a further development, Australia spinner Brad Hogg has been charged with making an offensive remark to two Indian players.
The ICC's actions seem to have calmed the stance of the Indian cricket board, who have now confirmed that the tour will continue.
The BCCI released a statement on Tuesday, which said: "The (working committee) of the BCCI took note of all relevant circumstances and developments and decided that the Indian team tour to Australia should continue for the present."
The statement, read to the press by BCCI treasurer N Srinivasan, went on to warn that the team could still return to India if Harbhajan is not exonerated.
It continued: "The ICC has clarified to the board that Harbhajan could play until the final disposal of the appeal.
"This is only an interim arrangement.
"The BCCI is of the categorical view that the matter will have to be finally resolved and the unfair allegation against an Indian player be set aside or withdrawn.
"The working committee reiterated that the ban imposed on Harbhajan is totally unacceptable.
"It further authorised the president (Sharad Pawar) to take all possible steps at his command and deploy all human and material resources available to get the player cleared of the obnoxious and baseless accusation."
The ICC have also sent chief match referee Ranjan Madugalle to Australia in a bid to "help the two captains in re-establishing an atmosphere of goodwill and mutual respect between the two teams".
The India squad, including Harbhajan, spent Tuesday playing volleyball and exercising on Bondi Beach as they waited for the matter to be resolved.