The Constitution of Ukraine (Ukrainian: Конституція України, romanized: Konstytutsiia Ukrainy) is the fundamental law of Ukraine. The constitution was adopted and ratified at the 5th session of the Verkhovna Rada, the parliament of Ukraine, on 28 June 1996.[1] The constitution was passed with 315 ayes out of 450 votes possible (300 ayes minimum).[1] All other laws and other normative legal acts of Ukraine must conform to the constitution. The right to amend the constitution through a special legislative procedure is vested exclusively in the parliament. The only body that may interpret the constitution and determine whether legislation conforms to it is the Constitutional Court of Ukraine.

https://en.wikipedia.org/wiki/Constitution_of_Ukraine

I'm still looking for the actual constitutional bit that says "no elections during war," or whatever phraseology has been passed around - Edit: Found it. (Links to original legal texts in this article.)

These regularly scheduled elections were disrupted by the state of martial law declared in 2022, at the start of the full-scale Russian invasion. This can be expected from a country fighting for its very existence, where significant portions of its territory are occupied. Martial law is established as a concept in the Ukrainian Constitution and last updated by the national legislature in 2015, before Zelensky entered politics.

Article 83 of the Ukrainian Constitution states that if the term of the Verkhovna Rada expires under martial law, it shall automatically be extended until a new Rada is seated following the end of martial law. Article 19 of Ukraine’s martial law legislation specifically forbids conducting national elections. Thus, for Ukraine to conduct elections while under martial law would be a violation of legal norms that predate Zelensky and the full-scale Russian invasion.

~~but assuming that's true,~~ Zelenskyy has nothing to do with whether or not elections happen. Having elections would be in violation of the constitution. ~~And Zelenskyy has nothing to do with amending the constitution, either; that's for the legislature to do.~~ Zelenskyy is following the law, as his office requires that he do.

Edit: I'm a bit wrong there. Article 93 reads:

The right of legislative initiative in the Verkhovna Rada of Ukraine belongs to the President of Ukraine, the People's Deputies of Ukraine, and the Cabinet of Ministers of Ukraine.

Draft laws defined by the President of Ukraine as not postponable, are considered out of turn by the Verkhovna Rada of Ukraine.

Which means that the President can put forward legislation for the parliament to vote on, even cutting to the front of the line. I bet this includes constitutional amendments.

But Article 19 Section 1 of the Ukrainian martial law legislation says no changes to the consitution and no national elections during martial law.