Rain has also been forecast for Wednesday's match between Australia and Pakistan in Taunton
Sri Lanka's World Cup match against Bangladesh was abandoned without a ball being bowled due to rain in Bristol on Tuesday.
The umpires' decision left tournament organisers with the unwanted record for the most number of abandoned games at a World Cup, surpassing the two each at the 1992 tournament in Australia and New Zealand and the 2003 edition in southern Africa.
It was the second successive World Cup match at Bristol that had fallen victim to bad weather, with Sri Lanka's group game against Pakistan at southwest county Gloucestershire's headquarters on Friday another no-result washout that did not witness a single delivery.
Rain has also been forecast for Wednesday's match between Australia and Pakistan in Taunton.
No reserve days have been scheduled for the 10-team round-robin stage, despite the well-known risks of rain during a British summer.
Asked whether there should be reserve days in the group phase, Bangladesh coach Steve Rhodes, a former England wicket-keeper, said: "Yes, I would (have them).
"I know logistically it would have caused problems. But we can put a man on the moon, so if we have to travel a day later, so be it."
Only one of three World Cup matches scheduled to take place in Bristol produced any play, champions Australia launching their title defence with a seven-wicket victory over outsiders Afghanistan.
Heavy overnight and early morning rain delayed the scheduled 10:30 am local time (0930 GMT) start of Tuesday's match.
And with rain continuing to fall, the umpires -- after several inspections -- bowed to the inevitable by calling the game off at 1:57 pm (1257 GMT).
Both sides received a point for the washout.
It was the second World Cup no-result in as many days after rain meant only 7.3 overs were possible in the match between South Africa and the West Indies in Southampton on Monday.