The day-ahead contract fell 0.40 pence to 33.10 p/therm by 1020 GMT.
The within-day contract dropped 1.15 p to 33.20 p/therm.
Zelenskiy said Ukraine and Russia had "unblocked" the issue of gas transit and that the countries' advisers would work on the details of an agreement.
Current deal between Russia and Ukraine that allows the transit of Russian gas via Ukraine to Europe expires at the end of this month.
"I think traders are pricing in some kind of an agreement," one gas trader said.
UK market is also pressured by a busy arrival schedule of liquefied natural gas (LNG) tankers.
At least 20 LNG cargoes are expected to unload at British terminals by Jan. 1.
UK gas market was undersupplied on Tuesday, with demand forecast at 274.7 million cubic metres (mcm) and supply at 267.2 mcm, National Grid data showed.
UK imports from Norway were expected to decrease by 10 mcm from Monday volumes to 81 mcm/day, Gassco data showed.
Flows from UK Continental Shelf were also predicted to fall by 6 mcm to 124 mcm/day.
Unplanned outage at Centrica's Rough terminal is expected to end today at midday.
Refinitive analysts said in a morning report that it was possible that the outage would be extended, however.
LNG sendout were expected 7 mcm lower on Tuesday, compared to Monday.
On the demand side, residential consumption and gas-for-power demand were expected to rise on Wednesday.
The January contract was down 1.15 pence at 37.05 p/therm.
The day-ahead gas price at the Dutch TTF hub was down 0.38euro at 13.35 euros per megawatt hour.
The benchmark Dec-19 EU carbon contract was down 0.03 euro at 25.10 euros per tonne.