Oklahoma City and several north Texas communities have been seeking to obtain water from the area to meet future needs.
Fallin commented on the timing of the lawsuit, noting a Congressional delegation reception with tribes is set for Sunday.
Fallin will host a reception at the Governor's Mansion for state, federal and tribal officials in honor of the visit to Oklahoma by members of the U.S. House Subcommittee on Interior, Environment and Related Agencies.
The subcommittee members are visiting Oklahoma and other states as part of research on tribal and federal government relations.
Joining the governor will be members of her cabinet, state lawmakers, members of the legislative Native American Caucus and representatives of tribal governments from across Oklahoma.
Among the federal officials scheduled to attend are U.S. Rep. Tom Cole, R-Moore; U.S. Rep. Mike Simpson, R-Idaho, chairman of the House subcommittee; U.S. Rep. Betty McCollum, D-Minnesota, a member of the subcommittee; Larry EchoHawk, assistant secretary for Indian affairs at the U.S. Department of the Interior; and Dr. Yvette Roubideaux, director of the Indian Health Service.