
zurückweisen
to reject
To refuse or not accept something, for example an application, an offer, or a request.
Das Gericht hat die Klage aus formellen Gründen zurückgewiesen.
The court rejected the lawsuit on formal grounds.
to reject / turn away
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to reject
To refuse or not accept something, for example an application, an offer, or a request.
Das Gericht hat die Klage aus formellen Gründen zurückgewiesen.
The court rejected the lawsuit on formal grounds.

to reject
To firmly deny an accusation, allegation, or criticism and reject it as untrue.
Der Minister wies die Korruptionsvorwürfe entschieden zurück.
The minister firmly rejected the corruption allegations.

to turn away
To refuse someone entry or send them away.
Mehrere Asylsuchende wurden an der Grenze zurückgewiesen.
Several asylum seekers were turned away at the border.
'Zurückweisen' (to reject / turn away) is a separable verb. In a main clause, the prefix 'zurück' goes at the end of the sentence. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Der Türsteher wies den Gast zurück.
The bouncer turned the guest away.
The verb consists of 'zurück' (back) and 'weisen' (to direct, to show). So the literal meaning is to send something or someone 'back in the direction' they came from. This helps explain all the meanings involving rejection.
Sie wies seine Hilfe höflich, aber bestimmt zurück.
She politely but firmly rejected his help.
The object of the sentence reveals the exact meaning: if you 'zurückweisen' (reject) a thing, e.g. an application, it means 'to refuse'. If you 'zurückweisen' (reject) a claim, e.g. an accusation, it means 'to deny'. If you 'zurückweisen' (turn away) a person, it means 'to send away'.
Der Antrag wurde aus formalen Gründen zurückgewiesen.
The application was rejected on formal grounds.
In the meaning 'ablehnen' (to reject/refuse), 'zurückweisen' is often used in formal, official, or legal contexts. It sounds stronger and more formal than a simple refusal.
Das Gericht wies die Berufung des Angeklagten zurück.
The court rejected the defendant's appeal.
When denying accusations or criticism, 'zurückweisen' is often intensified with adverbs such as 'entschieden' (firmly), 'scharf' (strongly), 'vehement' (vehemently), or 'kategorisch' (categorically).
Der Sprecher des Unternehmens wies die Gerüchte scharf zurück.
The company spokesperson strongly rejected the rumors.
to reject
Both verbs can describe an application, offer, or request as not being accepted. Ablehnen is the more general form; zurückweisen often sounds more formal and more decisive, especially in an official response. In neutral everyday situations, ablehnen is usually appropriate; for a clearly formal rejection, zurückweisen also fits.

Die Behörde wies den Antrag auf eine Genehmigung entschieden zurück.
The authority decisively rejected the application for a permit.
Die Behörde lehnte den Antrag auf eine Genehmigung ab.
The authority rejected the application for a permit.