In their first contact since the beginning of the war in Ukraine, US Secretary of State Antony Blinken said he pressed Russian Foreign Minister Sergey Lavrov to accept a proposal to free two Americans detained in Russia.

"We had a frank and direct conversation. I pressed the Kremlin to accept the substantial proposal that we put forward," Blinken told reporters.

Blinken said on Wednesday he planned to contact Lavrov in an attempt to free two Americans, basketball star Brittney Griner and former Marine Paul Whelan, and to follow up on a proposal made several weeks ago.

On Lavrov's reaction, the top US diplomat commented by saying, "I can't give you an assessment of whether I think things are any more or less likely."

"But it was important that he heard directly," Blinken said.

Blinken also pressed Lavrov on Russia honoring a Turkish-brokered proposal to ship grain out of Ukraine, as well as on Moscow's alleged plans to annex additional areas of Ukraine seized by Russian troops.

Blinken stressed that he told Lavrov that "the world will never recognize annexation" and that Russia would be hit by additional ramifications.

"It was very important that the Russians hear directly from us that that will not be accepted -- and not only will it not be accepted, it will result in additional significant costs being imposed upon Russia," Blinken said.

Elsewhere in his remarks, he claimed that Russia was preparing "sham referendums" to try to "falsely demonstrate that the people in these parts of Ukraine somehow seek to become part of Russia."

The votes would be part of Russian President Vladimir Putin's objective of "gobbling up as much Ukrainian territory as he can," he claimed.

Regarding Taiwan, US Secretary of State Antony Blinken expressed hope of managing differences over Taiwan with China after Beijing's warnings against a potential visit to the island by House Speaker Nancy Pelosi.

"It would be important as part of our shared responsibility to continue to manage this in a wise way that doesn't create the prospect for conflict and keeping open lines of communication on this issue," Blinken said.

Lavrov: Washington breaking its promises

On his account, Russian Foreign Minister Sergey Lavrov told Blinken that Washington was not living up to promises regarding the exemption from sanctions for the supply of food from Russia.

Lavrov outlined the details of the Istanbul agreements on lifting restrictions on the supply of Russian products for export and on Russia's assistance in the export of Ukrainian grain, stressed the role of US sanctions in the food situation, and also said that it was unacceptable to use the topic food for political purposes, as per the Russian Foreign Ministry statement.

"The situation in the sphere of ensuring global food security was thoroughly considered. Antony Blinken was briefed about the details of the 'package' agreement, signed on July 22 in Istanbul, on the transportation of Ukrainian grain from the Black Sea ports and on the facilitation of Russian exports of food and fertilizers," the Ministry said in a statement.

"The minister emphasized that the situation was being complicated by US sanctions, and the US promises to provide appropriate exemptions for Russian food supplies had not yet been implemented. It was indicated that the use of this problem by the 'collective West' in their geopolitical interests was unacceptable," the Ministry stressed.

Lavrov also told Blinken that Russia would achieve all of the objectives of its "special military operation" in Ukraine and that Western arms supplies would only prolong the conflict, according to a Russian foreign ministry read-out of the call.

Read more: US weapons to Ukraine “in a big black hole” - US official

Lavrov also told Blinken that "the continuous pumping of US and NATO weapons into Ukraine's armed forces...only prolongs the agony of the regime in Kyiv, prolonging the conflict and multiplying the casualties," as per the Russian Foreign Ministry.

Read more: Russia cautions West against "mindlessly pumping weapons" into Ukraine