VIENNA — Austria’s president praised the “elegance” of the country’s Constitution on Tuesday, seeking to calm concerns as the crisis that has torn apart Chancellor Sebastian Kurz’s right-wing coalition government accelerated, putting his future in doubt.

Mr. Kurz, who had sought an early election in September and is preparing to lead a minority government until then, now faces the prospect of a no-confidence vote that could eject him from power within days. A technocratic administration would then take over until elections could be scheduled, probably in June or early July.

The governing coalition, an alliance between Mr. Kurz’s conservatives and the far-right Freedom Party, began to unravel on Saturday, when a video emerged showing the far-right party’s leader discussing an exchange of favors with a woman claiming to be a Russian oligarch’s niece.

The days since have seen the once stable country rocked by political turmoil that could spell disaster for the ambitious young chancellor, once hailed as a rising star of Europe’s conservatives.