Interior Secretary James G. Watt's six-month running battle environmentalists took another turn for the worse yesterday when the National Wildlife Federation, the nation's biggest conservation group, called on President Reagan to fire him.

The organization's leaders accused him of working to undermine basic environmental protection laws and contended that conversations with key White House aides indicated that presidential support for Watt was "wanning."

The NWF attack on Watt is significant because the group, which includes many hunters and fishermen, is one of the most conservative of the environmental organizations and one Watt had counted most supportive of him. A poll of its membership, which produced overwhelming opposition to Watt's policies, indicated that they voted by more than 2-to-1 for Reagan last Novemeber.

In a letter to the president, federation officials denounced Watt's stewardship of natural resources and his "extreme views on exploitation." In calling for his dismissal they said they were seeking to work not against Reagan, but with him.

The executive vict president, Dr. Jay D. Hair, said: "After six months the evidence of Mr. Watt's unsuitability for the job he holds has become so overwhelming we are convinced the sooner he is releived of his duites the better it will be for our country and its resources."

Watt's reaction reportedly was amusement. He said the paid officials of the NWF had opposed Reagan's election and his confirmation.

The NWF's professionally conducted random survey of 4,000 of its 4.5 million members shows that of 11 Watt policies, including more offshore gas and oil leasing and less protection for endangered species of wildlife, 10 were overwhelmingly rejected.

The survey was undertaken after Watt challenged the NWF to consult its membership about him, and to study his actions rather than his rhetoric.

Hair said the NWF members found Watt's record "wanting in nearly every respect."

"In our dealings with the secretary, including two extensive meetings I have had with him, we found that he places a much higher priority on development and exploitation than on conservation," Hair said. "We have found that he is inflexible and unresponsive to ideas and entreaties from the conservation movement."

Hair said he had discussed Watt's handling of his job with White House officials, including one top presidential adviser, and was told that there was a difference between Reagan's approach to the environment and that of his interior secretary and that White House support for Watt was waning.