The ITF said it already had plans to transform the Davis Cup into an 18-team "world-class finale" at the end of the 2019 season and expressed disappointment that the men's governing ATP had decided to go ahead with its new, 24-team event.
"We do feel that this was an opportunity missed by the ATP to work together with the ITF in a beneficial and positive way for the whole of tennis," the ITF said in a statement.
Announcing the new World Team Cup earlier on Sunday, ATP president Chris Kermode said in a statement: "This event will enable us to kick off our season with a major team event, with minimal impact on existing players schedules at the start of the year."
Tennis Australia CEO Craig Tiley hailed it as "an exciting new era in men's tennis".
"The world's top players will continue to start their year in Australia in a format that we believe will deeply engage the fans across Australia and throughout the world," he said.
The competition is likely to be a part of the build-up to the Australian Open, which begins in mid-January.
A smaller World Team Cup was held from 1978 to 2012 in Duesseldorf, Germany. It offered no ranking points and suffered from being held a week before the French Open.
With an already crowded calendar, the ITF, which also runs the women's Fed Cup team event, said: "The continued success of Davis Cup is critical for our sport because the ITF is the only body reinvesting globally into the future development of tennis.
"It is the ITF, alongside our 210 member nations, that develops the pipeline of talent that competes on the men's and women's professional tours and that work relies on the investment created by Davis Cup."
It said ITF member nations would vote in August on the Davis Cup reforms, which addressed changes requested by the ATP player council.
The ATP said details of its new event would be made public "in due course".
(Reporting by Clare Fallon; Editing by Christian Radnedge/Gene Cherry)
