WASHINGTON — President Barack Obama warned Donald J. Trump against hiring Michael T. Flynn to be part of his national security team when Mr. Obama met with his successor in the Oval Office two days after the November election, two former Obama administration officials said on Monday.

Mr. Obama, who had fired Mr. Flynn as the head of the Defense Intelligence Agency, told Mr. Trump that he would have profound concerns about Mr. Flynn becoming a top national security aide, said the administration officials, who were briefed on the Oval Office conversation. Mr. Trump later ignored the advice, naming Mr. Flynn to be his national security adviser.

Mr. Flynn was forced out of that position after it was revealed that he had lied to Vice President Mike Pence about his conversations with the Russian ambassador to the United States, amid a continuing investigation into connections between the Russian government and the Trump campaign.

Mr. Obama and Mr. Trump met for the first time in the Oval Office on Nov. 10 in what both men later described as a cordial, 90-minute session in which the outgoing president pledged to do everything he could to support the transition to a new administration.

Mr. Flynn’s name came up during a broader discussion about personnel issues, the former administration officials said. Mr. Obama’s concerns about Mr. Flynn, which were first reported by NBC News, were largely about his management of the D.I.A. and predated the later concerns about his contacts with the Russian ambassador, Sergey I. Kislyak.

But one of the former administration officials said that Mr. Obama was also aware of Mr. Flynn’s well-publicized trip in 2015 to Moscow and other contacts with Russia.

The revelation on Monday about Mr. Obama’s warning came hours before Sally Q. Yates, the former acting attorney general, was scheduled to testify in the afternoon in front of a Senate committee that she later raised her own concerns about Mr. Flynn’s Russia contacts with the incoming Trump administration.

Mr. Trump blamed Obama officials on Monday, saying in two Twitter messages that it was his predecessor’s administration that gave Mr. Flynn a security clearance.

“General Flynn was given the highest security clearance by the Obama Administration — but the Fake News seldom likes talking about that,” Mr. Trump said.

In a second Twitter message, Mr. Trump added: “Ask Sally Yates, under oath, if she knows how classified information got into the newspapers soon after she explained it to W.H. Counsel.” An early version of the message misspelled “counsel.”