A House Appropriations subcommittee has handed a new challenge to President Carter in his attempt to cut back on federal water projects.

In approving the 1978 public works appropriations bill, the subcommittee last week not only provided funds for 17 of the 18 projects Carter wanted halted, but also added money for construction starts on 12 new dam and waterway projects.

Subcommittee Chairman Tom Bevili (D-Ala) said yesterday, "Certainly we all want to work with the President" on water projects. But he added that did not mean halting projects that had already been started or approved by Congress for construction.

A White House aide said yesterday the administration had not yet screened the 12 new starts approved by the subcommittee as it did during a March-April review of some 300 ongoing Corps of Engineers and Bureau of Reclamation projects.

Another middle 6 or 1 Carter aide said "the only way" to show Congress the President is serious about cutting down on the projects "is a veto. We're now in a game of chickent."

Bevill, on the other hand, said the subcommittee had been restrained in its funding of projects and proposed new starts. Last year Congress added 27 new construction starts, and 16 the year before.

"This is the lowest number of new starts six years," a subcommittee aide said.

At a subcommittee hearing in February, the Corps of Engineers said there were about 40 projects on which construction could begin.

Bevill said the new starts are all relatively small. The largest is an $83 million Mississippi River channel at Baton Rouge; the smallest a $3.5 million river basin in Texas.

The subcommittee acquiesced in only one Carter request to cut out all funding on a project - the $83.9 million Grove Lake dam in Kansas.

The subcommittee, however, did go along with some modifications in funding. On the $1.2 billion Central Arizona project, for example, three dams were dropped. Carter had suggested that compromise after it was originally put forward by some members of the Arizona congessional delegation.

On the controversial $436 million Garrison Diversion project in North Dakota, the subcommittee provided all the previously requested funds but added in its report that none of the money could be used to affect a river that flows into Canada.

Bevill said the President had told him "the Garrison project was the first thing mentioned" by Canada's Prime Minister Pierre Trudeau when he visited Washington.

Bevill said, however, "we saw no reason to stop," the other 17 projects Carter wanted halted, and he hoped Carter would go along with Congress on the 1978 funding.

"If the President wants the criteria for water projects changed," Bevill said, "the way to do it is by law, not canceling out approved projects,"

The full Appropriations Committee will take up the public works bill May 25 and Bevill expects it to reach the House floor June 10.