GENEVA, April 13--The United States and Britain proposed a prompt termination of atmospheric and underwater nuclear tests today, but the initial Soviet reaction to the proposal was cool.

The new move was designed to tackle test suspension on a step-by-step basis and thus salvage something from the three-power nuclear ban conference here. The Western powers hope agreement can be reached on the easiest part of the problem first, with attempts in later negotiations to widen the ban so as to include outer space and underground blasts.

Dulles' Fate Doubtful

WASHINGTON, April 13--President Eisen hower delayed a decision today on John Foster Dulles' future as Secretary of State.

Most administration leaders were gloomy about the prospects that Dulles could win his fight. They expected he would resign shortly, perhaps within a comparatively few days.

Sen. George Aiken (R-Vt.) said that unless Dulles is able to resume full-time work by the foreign ministers' meeting in Geneva, May 11, "I would expect he would resign."

Discoverer Launched

VANDENBERG AIR FORCE BASE, Calif.--America's second Discoverer satellite roared southward into polar orbit yesterday, setting the stage for a sigantic game of aerial catch in which planes may try to snatch its parachuting nose cone from the air.

At Cape Canaveral, Fla., last night an attempt to put two Vanguard satellites into orbit on a single launching vehicle failed when the second stage failed to ignite.