The Senate voted overwhelmingly yesterday to repeal the federal ban on interstate sales of handguns and other firearms as it approved, 79 to 15, a bill to ease gun controls enacted 17 years ago after the assassinations of the Rev. Martin Luther King Jr. and Sen. Robert F. Kennedy (D-N.Y.).

It also turned down a proposal to require a 14-day waiting period and police check before handguns could be purchased, and approved a new provision assuring a gun dealer advance warning of a compliance inspection.

The vote to lift the ban on interstate gun sales came when the Senate rejected, 69 to 26, a proposal from Sen. Edward M. Kennedy (D-Mass.) to retain the prohibition for handguns, including "Saturday Night Specials," while repealing it for rifles and other weapons often used for sporting purposes.

The bill, as proposed by Sen. James A. McClure (R-Idaho) and pushed by the National Rifle Association, would allow an out-of-state purchaser to buy any gun over the counter so long as the sale did not violate laws of the seller's or buyer's state.

"It's a law-enforcement issue -- a crime-control issue . . . . You don't use a 'Saturday Night Special' to save Bambi," Kennedy said, claiming support of several major law-enforcement groups for his effort to keep current gun-control legislation from being watered down.

Sarah Brady, wife of presidential press secretary James S. Brady, who was critically wounded during the attempt on President Reagan's life in 1981, wrote a letter to all senators this week opposing any easing of the current controls. The Reagan administration supports McClure's bill.

The Senate, under pressure from gun owners and dealers complaining that they are unduly restricted and harassed by current federal regulations, was clearly disposed to support the measure with modifications worked out earlier by its Republican leadership.

McClure's bill was cosponsored by a majority of all senators, and Kennedy's amendment split the Democrats evenly, as they tended to divide along regional lines. Maryland senators voted for Kennedy's amendment; Virginia's opposed it.

The compromise modifications, which the Senate approved earlier without dissent, deleted some of the bill's most controversial provisions, including language that critics interpreted as likely to invalidate laws restricting the transportation of guns in 20 states, including Virginia, and the District of Columbia.

Instead of voiding the state laws, the bill would bar prosecution under these statutes when a gun is unloaded and inaccessible, such as lying in the trunk of a car.

Other compromise provisions would bar importation of parts used in "Saturday Night Specials," modify language allowing sale of guns at temporary locations and drop a proposal to require a showing of illegal intent in order to prosecute.

The proposal for a waiting period for gun sales, advanced by Sen. Daniel K. Inouye (D-Hawaii), was rejected 71 to 23. The move to continue allowing compliance inspections without warning, pushed by Sen. Charles McC. Mathias Jr. (R-Md.), was defeated 76 to 18.

Similar legislation in the House, sponsored by Rep. Harold L. Volkmer (D-Mo.), has picked up 129 cosponsors but is bottled up in the Judiciary Committee. Its chances of passage are considered slim.