 Dalmiya and the ICC's Ehsan Mani disagree over the cash |
India want the Test championship programme to be extended to ease the pressure on players. The Board of Cricket Control in India (BCCI) is asking the International Cricket to increase the 10-year programme by another two years.
BCCI president Jagmohan Dalmiya said the schedule was "too cramped".
"Players are not getting any respite in between and are playing continuous cricket," he added.
The ICC's Test programme was launched in February 2001 to aid the long-term planning and marketing of the game.
 | To play countries in that period is too tough  |
It also provides more opportunities for weaker Test nations Zimbabwe and Bangladesh.
Each Test nation plays each other twice at home and twice away in the 10-year programme.
Dalmiya said: "To play countries in that period is too tough.
"It was decided by the board to request and represent to the ICC to have this programme spread over 12 to 14 years."
Meanwhile the BCCI has threatened to take the ICC to court if it is not paid money it says it is owed from the World Cup.
The BCCI says US$9m (�5.41m) should be paid by 1 November.
India, who reached the final, say the cash belongs to them.
But the ICC is awaiting the settlement of a claim over endorsement contracts by its commercial partner and marketing arm, Global Cricket Corp.
The corporation has filed a claim for damages because Indian players endorsed products from companies that competed with World Cup sponsors.
Dalmiya said the ICC was being "unreasonable and wrong" in holding back the board's share.
"The reason given by the ICC for holding back our money is frivolous," said Dalmiya.
"The ICC will have to pay us our money with interest by 1 November, failing which we will resort to arbitration."
The International Court of Arbitration in Lausanne, Switzerland, could be the venue of any legal action.
The ICC said it had suffered losses and faced being sued by sponsors because of the Indian players' actions.
But Dalmiya called the claims of damage "fictitious."