President Donald Trump’s proposed summit with Russia’s Vladimir Putin in Budapest appears farther off than initially hoped, with talks toward planning such a sit-down now “on hold,” a senior White House official told NBC News.

After Trump was briefed on what the senior official described as a “productive” call between Secretary of State Marco Rubio and his Russian Foreign Minister Sergey Lavrov on Monday, the president essentially pressed pause — believing that both sides in the Russia-Ukraine conflict were not ready to seriously talk peace.

“Secretary Rubio and Foreign Minister Lavrov had a productive call,” a second White House official said. “Therefore, an additional-in-person meeting between the Secretary and Foreign Minister is not necessary, and there are no plans for President Trump to meet with President Putin in the immediate future.”

Another phone call between Rubio and Lavrov is expected as soon as this week, a source familiar with the discussions told NBC News. The source did not rule out a future meeting, although no meeting is currently planned. The top U.S. and Russian diplomats are both expected to attend the Association of Southeast Asian Nations this weekend.

Earlier, the Kremlin denied it was holding up Trump’s latest push to end the war in Ukraine, and insisted it had not changed its demands ahead of possible talks.

The president had announced that Russia and the United States’ top diplomats would meet this week, with his own summit with Putin to follow in Hungary’s capital Budapest. Russian officials have now said there was no date set for either meeting.

“We cannot postpone what has not been agreed upon,” Deputy Foreign Minister Sergei Ryabkov told Russia’s TASS state news agency early Tuesday.

He was responding to a CNN report that the meeting between Rubio and Lavrov had been put on hold indefinitely. Ryabkov said there had been no clear agreement on when or where such a meeting might take place.

“Everything is in progress, internal work is ongoing. As new information becomes available, we will keep you informed,” he told state media journalists.

Kremlin spokesman Dmitry Peskov echoed Ryabkov’s comments when talking about the summit in Budapest.

“You can’t postpone something that hasn’t been agreed upon,” Peskov said in his daily briefing. “You heard statements from both the American side and our side that this may take time. Therefore, no precise timeframe was initially set,” he said.

On Tuesday, Lavrov confirmed that he and Rubio had spoken and discussed how to prepare a “framework for the next meeting” between Putin and Russia.

“The key point is not the venue or timing, but how we will proceed substantively on the tasks that were agreed upon and on which broad understanding was reached in Anchorage,” he said, referring to Trump and Putin’s meeting in Alaska in August.

The two agreed to continue the telephone contacts on how to “move forward in the right direction,” he added.

Lavrov said that the country’s position remains consistent with understandings reached between Putin and Trump during the Anchorage talks.

“Those understandings are based on the agreement achieved at that time, which President Trump very succinctly formulated when he said that what is needed is a long-term, sustainable peace, not an immediate ceasefire that would lead nowhere,” he said.

On Sunday, after both a call last week with Putin and then a meeting with Ukrainian President Volodymyr Zelenskyy in Washington, Trump said he supported the immediate halt to fighting as called for by Kyiv and its European allies.

For now, both sides should “stop at the battle line — go home, stop fighting, stop killing people,” he told reporters on board Air Force One. “They can negotiate something later on down the line,” he said.

Leaders of European nations, including Britain, France, Germany, Ukraine, and the European Union issued a joint statement Tuesday supporting Trump’s efforts to end the fighting, and suggesting that Russia appeared unwilling to pursue a peace agreement at this stage.

“We strongly support President Trump’s position that the fighting should stop immediately, and that the current line of contact should be the starting point of negotiations,” said the statement, published by the British government.

“We must ramp up the pressure on Russia’s economy and its defense industry, until Putin is ready to make peace,” it said.

In an interview with NBC News’ “Meet the Press” taped Friday, Zelenskyy urged Trump to get tougher with Putin and said he was ready to join their summit in Budapest.

Hungary’s foreign minister, Peter Szijjarto, was in Washington on Tuesday. He posted on Facebook: “We have some serious days ahead.”