A diplomatic row has erupted between Austria and Czechoslovakia after Czechoslovak border guards apparently crossed into Austrian territory and shot to death a refugee trying to escape to the West.

The Austrian government said it was prepared to believe the incident resulted from the impulsive actions of two naive or zealous guards. It demanded a full apology and assurances that such trespassing would never happen again.

But the Communist authorities in Prague rebuffed the protest and recalled their envoy to Vienna, Marek Venuta, on Nov. 13 to demonstrate pique over what was described as an "anti-Czechoslovak hate campaign" raging in Austria after the shooting.

Rude Pravo, the Communist Party daily, charged that Austria was responsible for frequent border violations "inspired by various centers of espionage."

Czechoslovakia's aggressive defense of the killing infuriated Austrian officials, who expressed open revulsion toward the absence of regret in Prague.

Austrian Foreign Minister Leopold Gratz said there could be no doubt that "the escalating crisis in bilateral relations was clearly triggered by the behavior of the Czechoslovak authorities."

The body of the defector, Frantisek Faktor, described as a railway worker in his early thirties, was discovered earlier this month near Gmuend, a town of 15,000 people split by the border.

Interior Ministry officials said Faktor was found lying 500 yards inside Austria, dead from a Czechoslovak bullet lodged in his back. Police collected 30 spent cartridges, also of Czechoslovak origin, in an area 200 yards on Austria's side of the border.

Czechoslovak authorities insist that the man was shot several hundred yards inside their own border but that he managed to stagger into Austrian territory before collapsing.

But Austrian doctors who examined the body said it would have been impossible for any human to run as much as 1,000 yards through the frontier's difficult terrain given the grievous nature of Faktor's wound, according to Andreas Rudas, an Interior Ministry official involved in the case.

"The doctors say it's remarkable that he could have walked even a few steps, let alone that distance," he said.

Rudas stressed that despite frequent border disputes with Czechoslovakia, this was the first occasion that Austrian officials have been able to produce compelling evidence of Czechoslovak border guards who ventured into Austrian territory to shoot a fleeing defector.

Austria maintains good border relations with Yugoslavia and Hungary, whose citizens do not require a visa to enter Austria, Rudas said.

But he said border tensions with the Czechoslovak authorities have become increasingly troublesome since the demise of Alexander Dubcek's reformist government in 1968 and his replacement by a hard-line regime following the Soviet-led invasion.

The winding frontier between the two countries has been fortified steadily in recent years with extra barbed wire, tank traps and more powerful lights. Czechoslovak border guards are said to receive bonus payments for each fugitive they capture or shoot.

The Austrian government, led by Socialist Chancellor Fred Sinowatz since May 1983, has tried to follow a conciliatory good neighbor policy, straddling East-West tensions.

Vienna has sought to emphasize its neutral status by avoiding defense commitments with the West and encouraging economic cooperation with its Eastern European neighbors.

But Czechoslovakia, more than any other Soviet Bloc country, including the Soviet Union, has engaged in an intensive propaganda campaign accusing Austria of renouncing solemn vows of neutrality taken when it regained its independence in 1955.

Sinowatz, who was scheduled to begin a four-day trip to Moscow this weekend for talks with Soviet leaders, was also considering an invitation to visit Prague next year in an effort to improve relations.

But the controversy over the border shooting has thrown the Prague trip into jeopardy, Foreign Ministry officials said.

In an effort to avoid exacerbating the crisis, Austria has refrained from pulling its ambassador out of Prague to match Czechoslovakia's protest. Prague was the last Soviet Bloc capital to agree to exchange ambassadors with Austria after the war.

The only punitive action taken so far by Vienna has been Gratz's decision to postpone cultural exchanges until the crisis is resolved.

Meanwhile, Austrian police have stepped up their border patrols, an Interior Ministry official said, to "show our population near the frontier that we intend to protect them from future incidents of this kind."