By Jeremy Diamond, CNN

(CNN) -- President Donald Trump and Russian President Vladimir Putin discussed the possibility of meeting at the White House during a phone call last month, the White House confirmed on Monday.

"As the President himself confirmed on March 20, hours after his last call with President Putin, the two had discussed a bilateral meeting in the 'not-too-distant future' at a number of potential venues, including the White House," White House deputy press secretary Raj Shah said in a statement.

Shah's comment came after Yuri Ushakov, an aide to Putin, said Trump "offered to hold the first meeting in Washington, in the White House."

"If everything goes well, I hope that the Americans will not give up their proposal to discuss the possibility of holding the summit. When our presidents spoke on the phone, Trump offered to hold the first meeting in Washington, in the White House," Ushakov said during a briefing on Monday.

But Putin spokesman Dmitry Peskov appeared to deny the story soon after it broke, responding to a text from CNN's Matthew Chance asking for confirmation by replying: "No. Nothing specific yet. Contacts on this issue are yet to start. If ever ..."

Soon after speaking with Putin on March 20, Trump told reporters that he had a "very good call" with Putin and said he suspected "that we'll probably be meeting in the not-too-distant future to discuss the arms race, which is getting out of control."

"So I think probably we'll be seeing President Putin in the not-too-distant future," he said.

Tensions between the US and Russia have only escalated in the two weeks since that call, with Trump expelling 60 Russian diplomats the US believes were intelligence agents in response to Russia's alleged use of a nerve agent to poison a former Russian spy in the United Kingdom.

Russia retaliated with a similar move, expelling 60 American diplomats and ordering the closure of the US consulate in St. Petersburg last week.

The tough US action was followed with silence from Trump, who has yet to publicly comment on his decision to punish Russia for its alleged use of a nerve agent on British soil.

Facing criticism for failing to raise the nerve agent poisoning during the call and instead congratulating Putin on his re-election, Trump tweeted last month that "getting along with Russia (and others) is a good thing, not a bad thing."

"They can help solve problems with North Korea, Syria, Ukraine, ISIS, Iran and even the coming Arms Race. Bush tried to get along, but didn't have the "smarts." Obama and Clinton tried, but didn't have the energy or chemistry (remember RESET). PEACE THROUGH STRENGTH!" Trump tweeted the day after his call with Putin.