The Russian leader is demanding Ukrainian concessions in return for halting his army's invasion but granting him those demands would amount to rewarding the country that started the fighting, Kaja Kallas said.
The recent talk about handing Putin concessions was "exactly the trap that Russia wants us to walk into", Kallas said in an interview with the BBC on Friday.
"I mean, the discussion all about what Ukraine should give up, what the concessions that Ukraine is willing to (make), whereas we are forgetting that Russia has not made one single concession and they are the ones who are the aggressor here, they are the ones who are brutally attacking another country and killing people," she said.
US-led peace efforts have struggled to get traction, despite US President Donald Trump discussing the war with Putin in Alaska last week before hosting Ukrainian President Volodymyr Zelenskiy and European leaders at the White House on Monday.
Numerous details for a formal peace proposal need to be hammered out.
Meanwhile, Russia has continued to attack Ukraine and has raised objections to some key Ukrainian demands.
Establishing postwar Western security guarantees for Ukraine, which Kyiv insists are needed to deter another Russian attack, is under discussion by a variety of countries, Kallas said, noting that "it does sound like we are some way off in terms of pinning that down".
"Russia is just dragging feet. It's clear that Russia does not want peace," Kallas said.
"President Trump has been repeatedly saying that the killing has to stop and Putin is just laughing, not stopping the killing, but increasing the killing."
Ukraine, meanwhile, has hit back at Russia with long-range weapons that are targeting infrastructure supporting Moscow's war effort.
It has hit oil refineries, among other targets, and Russian wholesale gasoline prices have reached record highs in recent days.
Ukrainian forces on Friday targeted the Druzhba oil pipeline in Russia, hitting the Unecha oil pumping station in the Bryansk region, according to the commander of Ukraine's Unmanned Systems Forces, Robert Brovdy, also known as Magyar.
The Druzhba pipeline starts in Russia and takes oil through Belarus and Ukraine to Slovakia and Hungary.
In Russia, a section of it goes through the Bryansk region and the Unecha district.
Ukraine fired HIMARS rockets and drones at the region in a combined attack, Bryansk regional governor Alexander Bogomaz said in a Telegram post.
The pipeline supplies Hungary with more than half of its crude oil.
Hungarian Foreign Minister Peter Szijjarto wrote on Facebook on Friday that the Druzhba pipeline had been attacked "for the third time in a short time".
"This is another attack on the energy security of our country. Another attempt to drag us into war," the minister wrote.
Hungary under Prime Minister Viktor Orban has taken a combative stance toward both Kyiv and its EU backers while most EU countries have offered political, financial, and military support to Kyiv.
Slovakia and Hungary are the only remaining EU member states still receiving oil from Russia.
