Rudolph W. Giuliani, a lawyer for President Trump, speaks during a campaign event for a congressional candidate in New Hampshire. (Charles Krupa/AP)

President Trump’s lawyer Rudolph W. Giuliani on Monday sought to clarify his head-scratching assertion over the weekend that “truth isn’t truth,” writing in a morning tweet that he was referring to instances where two people make contradictory statements.

“My statement was not meant as a pontification on moral theology but one referring to the situation where two people make precisely contradictory statements, the classic ‘he said she said’ puzzle,” Giuliani said. “Sometimes further inquiry can reveal the truth other times it doesn’t.”

Giuliani’s attempt at clarification was prompted by an appearance Sunday on NBC’s “Meet the Press,” during which he and host Chuck Todd discussed the circumstances under which Trump would submit to an interview by special counsel Robert S. Mueller III.

Giuliani continued to argue that Mueller is trying to trap Trump into committing perjury as part of an investigation into whether the president has obstructed the probe of Russian interference in the 2016 presidential election.

“When you tell me that [Trump] should testify because he’s going to tell the truth and he shouldn’t worry, that’s so silly — because it’s somebody’s version of the truth. Not the truth,” Giuliani said.

Todd responded, “Truth is truth.”

“No, it isn’t truth. Truth isn’t truth,” Giuliani said.

The exchange was heavily featured on Monday morning news shows, with pundits comparing Giuliani’s assertion with White House adviser Kellyanne Conway saying earlier during Trump’s tenure that then-press secretary Sean Spicer had presented “alternative facts.”

Giuliani has said he fears Mueller would be more inclined to rely on testimony provided by former FBI director James B. Comey, whom Trump fired, than that of the president. If so, Giuliani has said, Trump could be accused of perjury even if he’s telling the truth.

Following Giuliani’s Sunday appearance on “Meet the Press,” Comey took to Twitter, writing: “Truth exists and truth matters.”

“Truth has always been the touchstone of our country’s justice system and political life,” Comey said. “ People who lie are held accountable. If we are untethered to truth, our justice system cannot function and a society based on the rule of law dissolves.”

On Monday, Giuliani responded to Comey.

“Since proven leaker Comey is now sanctimoniously lecturing us on truth, I can say sometimes the truth is clear it’s the opposite of what Jim Coney is saying,” Giuliani wrote on Twitter. “His disgraceful performance with the FBI makes him the last person who should pontificate on truth.”