The two countries have been unable to decide whether Tests or One-day Internationals -- or both -- should be played during South Africa's tour of India in November.
The United Cricket Board of South Africa (UCBSA) has expressed unhappiness over the itinerary submitted by India, saying the Indians were indifferent towards the tour.
But Dalmiya, a former ICC president, said the 10-year schedule drawn up for Test nations by the sport's world governing body was causing problems in drawing up the itinerary.
"The real problem is that we are having to squeeze in a two-month schedule into a one-month capsule," he said on Tuesday.
"If I have to blame someone, it would be the ICC for the blunder in drawing up the 10-year schedule."
India are due to host world champions Australia for four Test matches between October 1 and November 7, while South Africa host England from December 5.
That leaves less than a month to squeeze in South Africa's tour of India in November, not enough time to play the scheduled three Tests and seven One-dayers.
Dalmiya said he had suggested that three Tests be held, but South Africa insisted on playing only the seven One-dayers in the available period so that they could return home in time to ready for the England series.
"The South Africans have declined to postpone England's tour by a week or two, which gives us less than a month to organise something," Dalmiya said.
"But it's not as serious as is being made out in the media. I am meeting UCBSA president Ray Mali in Dubai on Thursday and I am sure a solution will be found."
South Africa have not played in India since 2000, a tour that ended in controversy when Delhi police charged the then South African captain Hansie Cronje of trying to fix matches.
The UCBSA are worried that Herschelle Gibbs and Nicky Boje, two other players named by the Delhi police in the Cronje chargesheet, could be arrested or questioned during the November tour and wanted the BCCI to guarantee that no action will be taken against the players.
Dalmiya said he was unable to give a guarantee saying the BCCI had no jurisdiction in police matters.