A furor touched off by an interview with visiting House Foreign Affairs Committee Chairman Clement Zablocki (D-Wis.) has soured Greek-U.S. relations at a critical point in negotiations on the future of the American military bases in Greece.

The "Zablocki affair," which has dominated the front pages of Athens' strongly anti-American newspapers for the past few days, began Tuesday night with an interview over state-controlled Greek television. The interview came just one day before the start here of the third round of talks on the bases between Greek Foreign Undersecretary Yiannis Kapsis and U.S. negotiator Reginald Bartholomew.

In the interview, Zablocki raised the prospect of a shift of the U.S. bases from Greece to Turkey, and speculated on the consequences of this on Greek security in the Aegean, where Athens accuses Turkey of pursuing an expansionist policy.

In newspapers the next morning, Zablocki was sharply criticized for his comments. Columnists appeared to take particular exception to his remark--for which there is no precise Greek equivalent--that a Greek shutdown of the bases might be tantamount to "cutting off one's nose to spite one's face."

The Greek Socialist government is committed to working out a timetable in the current negotiations for eventually closing the bases. The dispute took on new life Wednesday night when, at an informal gathering at the residence of the American ambassador, Zablocki told reporters that Prime Minister Andreas Papandreou, in a private meeting, had personally apologized for the hostile press reaction to the interview.

Government spokesman Dimitris Maroudas later that night vehemently denied Zablocki's claim of a Papandreou apology as "absolutely untrue." Maroudas added that "remarks of this sort undermine bilateral relations and create a somber climate around the negotiations on the bases."

The acrimony surrounding the Zablocki episode is seen by analysts here as symptomatic of a new, more difficult phase in U.S.-Greek relations. This comes as the two sides move deeper into the negotiations for a new defense and economic cooperation agreement that will determine the future of the four U.S. bases on Greek soil.

The talks, which moved into their third round this week, are now expected to last well beyond the original informal nine-month deadline, possibly into 1984.

The consensus among analysts is that the most critical phase of the negotiations will involve the discussion of technical details of the bases' operation and the economic exchanges for their continued function. The first two rounds of talks were on a general level, to establish the initial positions on both sides.

The United States reportedly wants these details to be discussed on the level of technical experts. For Greece this would mean expanding the current negotiating team, which now includes only Kapsis, a former leftist journalist who has been Papandreou's chief aide on the bases.

In the first two rounds, completed last year, Greece proposed a $1 billion annual rent by the United States for the bases and the shutdown of the Hellenikon airbase on the outskirts of Athens on the grounds that it services spy planes conducting electronic surveillance on non-NATO countries friendly to Greece.

Both these requests reportedly were rejected by Washington in December. Sources close to the negotiations also said there have been no discussions so far on the possibility of closing the base.

Papandreou remains publicly committed to the eventual removal of the bases from Greece on the basis of a so-called "timetable" of 10 or 12 years.

Under the 1953 U.S.-Greek agreement establishing the bases, their operation is linked directly to Greece's membership in NATO. A base shutdown would have to be accompanied by a Greek pullout from the alliance.

Leaving NATO has long been part of the policy of the Greek Socialists, who took power 1 1/2 years ago, but the link between NATO membership and the presence of the U.S. bases has never been publicized here.

There are four main U.S. military bases in Greece, as well as a number of auxiliary military installations throughout the country. In addition to Hellenikon, the major bases are Nea Makri, on the northern outskirts of Athens, and Heraklion and Souda Bay on the island of Crete.