WASHINGTON — Insisting he would “love to get along with Russia,” President Donald Trump defended Thursday his attempts to seek warmer ties with Moscow even as three top advisers raised major caution flags about cooperating with President Vladimir Putin’s autocratic government and military.

Questions about his administration’s controversial outreach to Russia dominated a sometimes-raucous White House press conference, and Trump denied that he had any investments, debts or even contacts there, saying, “I’ve done nothing for Russia.”

“I have nothing to do with Russia,” he said. “I have no deals there. I have no anything.”

But he was less definitive when repeatedly pressed to say whether members of his campaign team or other associates had been in contact with Russian intelligence officials during last year’s presidential race, an issue now under FBI investigation.

“Nobody that I know of,” the president said. He called questions about the issue a “ruse” and “fake news.”

After mixed signals from the White House, Trump confirmed that he had asked national security adviser Michael Flynn to resign this week after it became clear the retired Army general had lied about his phone calls to Russia’s ambassador.

“He didn’t tell the vice president of the United States the facts. And then he didn’t remember. And that just wasn’t acceptable to me,” he said.

He also blamed what he called “fake news” for perhaps ruining chances to improve relations by reducing his negotiating room. “I think Putin probably assumes he can’t make a deal with me anymore,” he said.

Trump’s comments are unlikely to dispel the storm of criticism on Capitol Hill and bipartisan calls for congressional investigations into whether Trump knew about Flynn’s calls, or if anyone else was improperly communicating with Russian authorities.

Several top advisers offered less enthusiastic praise for Russia.

At NATO headquarters in Brussels, Secretary of Defense James Mattis appeared to push back against Trump’s calls to join forces with Moscow in the war against Islamic State, saying Russia needs to “prove itself first” before the Pentagon would collaborate with Russian forces.

Secretary of State Rex Tillerson separately held his first meeting with Russia’s foreign minister, Sergey Lavrov, at a G-20 forum in Bonn, Germany. Tillerson said he urged Moscow to withdraw its troops from Ukraine, noting that the two countries don’t always “see eye to eye.”

Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, sat down with his Russian counterpart in Baku, Azerbaijan, the first such meeting since Russia seized Crimea and began backing an armed insurgency against the U.S.-backed government in Ukraine in 2014.

Concerns about Trump’s strategy on Russia have overshadowed much of the administration agenda. Trump has fed those concerns because he has consistently praised Putin and has continued to challenge or disregard U.S. intelligence and military assessments on the Kremlin’s role in the U.S. election, Syria, Ukraine and elsewhere.

Russian President Vladimir Putin said in a televised address Thursday to the Federal Security Service intelligence agency: “It’s in everyone’s interest to resume dialogue between the intelligence agencies of the United States and other members of NATO. It’s absolutely clear that in the area of counter-terrorism all relevant governments and international groups should work together.”

Mattis said that wasn’t possible given Russia’s military incursion in Ukraine and its humanitarian violations in Syria.

“They have to live by international law just like we expect all mature nations to do,” Mattis said. “We will engage politically. We’re not in a position to engage on a military level.”

Lavrov took a question from a reporter, who asked if he was concerned about turmoil in Washington, which stems in part from CIA and FBI warnings that Russian intelligence services sought to help swing the election to Trump.

“You should know we do not interfere in the domestic matters of other countries,” Lavrov said.

william.hennigan@latimes.com