Russian Federation seized Crimea in March 2014 after sending in troops, taking over key facilities, and staging a referendum deemed illegitimate by at least 100 countries in the United Nations. Ukraine has offered the regions autonomy under its rule.
The U.S. and Russia have been on opposing sides of the conflict in Ukraine, unleashed after a popular uprising against a pro-Russian president and Russia's annexation of Crimea in 2014.
"This issue was discussed", Antonov said, apparently referring to the conflict itself and not a proposal for a referendum.
Bloomberg said Putin was proposing a ballot of residents on the status of the two territories, carried out under worldwide auspices.
Hours after Antonov spoke, the White House shot down the idea, saying the Trump administration "is not considering supporting" such a referendum.
The Russian leader said that during his "very successful" one-on-one meeting, Trump paid "special attention" to the issue, "and I would like to confirm that Russia is interested in this development and will act accordingly".
During a joint news conference after their summit this week in Finland, Putin used soccer metaphors and was handed a soccer ball that he tossed to Trump. "We held a referendum in strict compliance with the United Nations charter and worldwide legislation. For us, the case is closed", he said.
Last month Trump appeared to leave the door open to the USA recognising the annexation.
At Monday's news conference, Putin described the proposal when he was asked about the possible extradition of 12 Russian intelligence officers indicted in the United States on charges of meddling in the 2016 election by carrying out cyber attacks on Democratic Party networks.
Putin told Russian diplomats on Thursday that US-Russian relations are "in some ways worse than during the Cold War", but that the meeting with Trump allowed a start on "the path to positive change".
Sergei Aksyonov, the governor of Crimea, told the Russian state-run news service RIA Novosti: "I am positive that [Putin] is doing everything in his power to [get the U.S. to] recognise Crimea [as a Russian region] and lift the sanctions. The first step was made, let's wait for the results now".
Trump tweeted that the two men discussed Ukraine but has not mentioned a referendum or revealed specifics of the Ukraine discussions.
Russia is ready to discuss a proposed new meeting between Russian President Vladimir Putin and his US counterpart Donald Trump, Interfax news agency cited Russia's ambassador to the United States, Anatoly Antonov, as saying on Friday.
"It was one of the most insane things I've ever heard coming out of his mouth", Browder told Bolduan.
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