Supporters of legislation that would give veterans the right to sue over denied benefits said yesterday that they will urge the Senate to add the controversial provision to legislation elevating the Veterans Administration to a Cabinet-level department.

The provision, which proponents say would give veterans "their day in court" and extend a right granted most federal welfare recipients, has been passed four times by the Senate, but has died each time in the House Veterans Affairs Committee.

Rep. G.V. (Sonny) Montgomery (D-Miss.), the committee chairman and a champion of the bill making the VA a department, said last night that if the Senate adds the judicial review provision to the House-passed departmental bill, it could end the decades-long effort to create a Department of Veterans Affairs.

"I can't speak for the administration, but I know they are violently opposed to judicial review," Montgomery said in an interview. He said that it was likely that President Reagan, who announced his support for the departmental bill in November, would veto legislation that includes judicial review.

Montgomery, who vehemently opposes the court-review provision, said he did not know what he would recommend to Reagan if the provision is attached to the bill. "You'll have to give me a minute to think about that," he said.

But he said that he did not believe Congress would enact judicial review for veterans "as long as the major veterans organizations are opposed to it."

Supporters of the judicial-review legislation said, however, that they believe they can mount a successful argument for tying the provision to the departmental status. Rep. Ted Weiss (D-N.Y.), who raised the issue during a House Government Operations subcommittee meeting yesterday, said he understood the provision should have "very strong" support in the Senate.

Proponents began to make the case before Weiss's subcommittee, producing a number of what staff members called "horror stories" about the way the VA handles claims. Raising questions about what Weiss called "serious deficiencies" in the VA, he produced accounts of seriously ill veterans who were denied benefits and VA officials who told of pressures to under-report errors and of being paid bonuses to review claims in as little as 20 minutes.

All the evidence, Weiss said, poses questions of whether Congress should create a new department without the same rights of court appeals allowed in other departments.

The VA and the Reagan administration have voiced strong objections to court review, saying it would cause the VA's budget to soar dramatically and force the agency to drastically alter what VA officials said yesterday has been a successful and "nonconfrontational" manner in which veterans' claims are considered. The administration has cited a Civil War-era law that limits the amount of legal fees a veteran may pay an attorney to $10, a level so low that few lawyers represent veterans before the VA.

Yesterday, a quadriplegic Vietnam-era veteran said he had been denied benefits seven times for injuries from a fall from a VA hospital bed to which he was supposed to have been strapped. The straps were not properly attached, and Ray Michael (Mike) Reed, who is confined to a wheelchair and linked to a respirator, said nurses ignored his pleas not to be moved.

Despite what his lawyer said was uncontradicted evidence that the fall worsened his condition, the VA has repeatedly turned aside his requests for aid. "It's my opinion that Mike never stood a chance of overcoming the institutional bias" of the VA and winning his claim, said attorney William G. Schaffer of Washington, who is representing Reed on a pro bono basis.

Two former members of the VA's Board of Veterans Appeals, the court of last resort for such cases, refused to side with Reed's complaint yesterday. But they did voice serious complaints about the board's operations, accusing chairman Kenneth E. Eaton of "stacking" some appeals panels with conservatives and paying bonuses to individuals who hurriedly review cases.

VA officials denied any wrongdoing, and R.J. Vogel, the VA's chief benefits director, told Weiss, "We seem to have become the chief whipping post for judicial review."