In the title story of Etgar Keret's fifth collection, a writer is confronted by a series of guests: all armed, each wanting to hear a story. As he tries to satisfy their demands, a gun against his head, the narrator ruefully reflects, "I bet things like this never happen to Amos Oz or David Grossman". It's a slyly comic aside that also serves as a point of differentiation. Keret may have glowing testimonies from the likes of Salman Rushdie, Yann Martel and Oz himself, but is yet to achieve the huge international status afforded his fellow Israelis. While Suddenly, a Knock on the Door is unlikely to raise Keret to such a rarefied field, it remains a maddening, abruptly moving and effortlessly funny collection.

Keret's stories explore the shaded space between joke and fable, between human understanding and the impossibilities of the world. The language is simple, almost brusque; the short narratives often occupy fewer than ten pages. They read as encounters, Keret choosing to leave a story hanging when so much more could have been exposed, or beginning tales so far into the action or emotion that it's almost over before you know where you are. It is a risky strategy, but one that forces the reader to mull on what has gone before. In Keret's hands, it is a winning formula.

Much of the joy in reading Keret comes from his unexpected shifts. Stories may begin as a man pitching a new board game to a multi-national corporation, a childhood lie, a son's anger at a grandmother, a lover's strangely vocal orgasm, but they are unlikely to end up anywhere approaching their obvious trajectory. Underpinning all of these tricks and sleights of hand, however, is a deep concern with the tensions between public and private, with the thoughts we have about ourselves versus other people's perceptions.

In some stories this is expressed via Kafkaesque transformations (into a haemorrhoid, or a beer-guzzling German); in others, just a simple first-person narrative that subtly exposes delusions. The opening to "Bitch" for example – "Widower. He loved the sound of that word so much, loved it but was ashamed that he loved it, but what can you do, love is an uncontrollable emotion" – places us immediately into an uncomfortable male quandary: what is thought against what is considered acceptable.

Keret's great skill is compressing these emotions into flights of absurdist imagination. "What, of this Goldfish, would you ask?" amuses then darkens into something both violent and affectingly sad; "Teamwork" is written with humour laced with a palpable underlying threat. These are stories that repay close reading; that offer more despite their simplicity.

Keret can be infuriating when stopping a story earlier than one would like, and some do feel inconsequential, but "Surprise Party", "Lieland", "September all Year" and "A Good One" are of an emotional innovative and linguistic power that few can match. Clever, relevant and oddly resonant, Suddenly, a Knock on the Door is Keret's best, most mature work and the perfect introduction to his sad, strange and moving fiction.

Stuart Evers's 'Ten Stories about Smoking' is published by Picador