Washington (CNN) President Donald Trump and Russian President Vladimir Putin appear to have had more sustained contact with each other in the past two weeks than at any time since 2016, as the Kremlin tries to use the coronavirus pandemic and close personal ties between the two leaders to normalize long-strained relations with Washington.

The two leaders spoke on the phone at least four times over a two-week period, beginning March 30 and ending on Sunday, a record pace for publicly known phone calls between the leaders, according to a CNN tally.

Official readouts of their conversations indicate the leaders discussed the coronavirus pandemic and a price war that destabilized the oil markets. The flurry of phone calls follow a Kremlin campaign urging US-Russia cooperation against the coronavirus that used news outlets Trump follows, said Andrew Weiss, a vice president for studies at the Carnegie Endowment for International Peace.

The calls have taken place as both Trump and Putin face domestic political challenges and offer the embattled leaders a way to claim wins. But analysts such as Weiss warn that Putin's outreach involves risks to the US.

'An end run'

"Reaching out to the United States ... is part of part of Putin's long-term plan to basically undermine the credibility of the United States as an important stalwart player in the global system, to undermine our alliances, and then to create as many lasting sources of tension between Donald Trump and his own national security team," Weiss told CNN. "The more that Russia succeeds in doing that, the less pressure Russia itself is likely to face from a unified western camp."

Putin's appeal to Trump is meant to be an "end run around the US national security bureaucracy, the State Department, the Pentagon, the intelligence community," which are far more distrustful of Moscow than the President is, Weiss said.

US-Russia relations have been complex since Trump became president. Though his relationship with Putin has been warm, Washington has slapped Moscow with tough sanctions for its invasion of Ukraine, interference in the 2016 election, other malicious cyber activities, human rights abuses, use of a chemical weapon, weapons proliferation, illicit trade with North Korea, and its support for Syria and Venezuela.

Tensions occasionally spill outside the political realm.

On Wednesday, the US Navy said a Russian Su-35 jet performed an "unsafe" intercept of a US P-8 surveillance aircraft while it was flying in international airspace over the Mediterranean Sea., putting US pilots and crew at risk.

The same day, Russia conducted a test of an anti-satellite missile that Space Command commander Gen. John W. "Jay" Raymond said, provides "further proof of Russia's hypocritical advocacy of outer space arms control proposals designed to restrict the capabilities of the United States while clearly having no intention of halting their counterspace weapons programs."

The tension has impeded cooperation on a number of fronts, including any progress on Americans detained by the Russians and the extension of the last remaining nuclear arms control treaty, New START, which expires in February 2021.

On Friday, Secretary of State Mike Pompeo told Russian Foreign Minister Lavrov that any renewal of the New START Treaty will have to include China, a condition that is widely seen as a way to scuttle the deal and lay the blame on Beijing. China has a much smaller nuclear arsenal than either the US or Russia and has no incentive to sign on to a pact that curbs its arsenal at levels far below its geopolitical rivals.

And Congress is now readying still more sanctions, including a bill targeting Russia's oil sector and other legislation meant to punish ongoing and future election interference

But Trump's stance toward Moscow has been much less hostile than that of Congress and some members of his administration.

Putin "has basically shown the rest of the US government that their views on Russia don't matter, that he has direct access to the US president."

Angela Stent, the director of Georgetown University's Center for Eurasian, Russian and East European Studies, said that Putin's contacts with Trump reflect a well-established pattern. Stent and other analysts say Trump and Putin have often squeezed out US officials when they've met or had discussions.

"Obviously as we've seen, Trump and Putin have met and discussed things together where the rest of the people were not in the picture," Stent said, pointing to the leaders' first summit in Hamburg where the leading White House official on Russia, Fiona Hill, wasn't invited to the meeting, as is customary.

"This has been characteristic of Trump and Putin the times they've met. We still don't know what they discussed in Finland," she said, pointing to the July 2018 summit in Finland in which Trump and Putin met alone with only their translators, a highly unusual breach of standard practice.

Matt Rojansky, director of the Kennan Institute at the Wilson Center, points out that this dynamic is likely driven by Trump's distrust of the US bureaucracy.

Referring to the criminal investigation into whether Trump or his campaign associates conspired with the Kremlin to win the 2016 presidential election, Rojansky said, "we have a President who doesn't trust substantial chunks of his own administration because of the whole experience of Russiagate and impeachment. That more than anything" is affecting the way the two leaders interact, he said.

"The normal firebreaks of a policy process will not necessarily work here," Rojansky said.

Siding with Russia

Never before has Trump been in such in such regular, publicly disclosed contact with the Russian strongman. Trump and Putin have spoken on the phone at least 16 times and met face-to-face at least six times, according to CNN's tally. Their communications often increased up during moments of crisis, like the OPEC conflict this month, and previously after a foiled terrorism plot in 2017.

The Trump-Putin relationship has always been a point of intrigue, largely because of Trump's unorthodox Russia-friendly views and because of the investigation into possible 2016 collusion between the Trump campaign and Russia.

Over the years, their conversations have included a mixture of routine and atypical moments.

They have worked together on ending the conflict in Syria, and they have discussed ways to reduce nuclear tensions in North Korea -- two areas of foreign policy where past US leaders, including former President Barack Obama, also tried to work with the Russian government.

But the relationship hit a low point when Trump and Putin met in Helsinki. Trump disavowed US intelligence about Russian meddling in US elections and publicly accepted Putin's denials. When Trump returned from the summit, he was met with bipartisan backlash, and his controversial comments were invoked at his impeachment trial this year.

Stent, who is also a senior fellow at the Brookings Institution, pointed to Russian political pressures as one reason for Putin's outreach.

A month ago, Russia was refusing to make a deal with Saudi Arabia over oil supplies, a standoff that sent oil prices plunging.

Those plummeting oil prices, a fall in the value of the ruble and then the pandemic began to hit the Russian economy, which could contract as much as 20% this year, Stent said. The pandemic meant that Putin has had to postpone a referendum, set for later this month, that is meant to keep him in power until 2036. The combined crunch forced Russia to come to an agreement with OPEC and drove Putin's popularity rating down as well.

Tatiana Stanovaya, a non-resident scholar at the Carnegie Moscow Center, told CNN that the constellation of events now "present Putin's system with the worst crisis of all time."

Stent said that Putin's calculus in reaching out to Trump might be that "if Russia is seen to be treated by the US as a major player and relations improve, maybe that will help him."

She notes that the US-Russia relationship has always been compartmentalized, with some areas of cooperation and some of competition. "I think you just have to be clear eyed about what it is you're cooperating on and understand there are other things you can't cooperate on," Stent said.

Rojansky said the Kremlin is "of course" using the virus and the call to cooperate to serve its goal of normalizing relations. "But that doesn't mean the case for international cooperation amid this pandemic is wrong," he added.

Referring to an CNBC op-ed, written by a Putin ally, Kirill Dmitriev, calling for cooperation to fight coronavirus, Rojanksy said it was "slick, but it flies a moral flag and recalls dark hours when grand cooperative undertakings were needed."

Rojansky said there is room for Washington to take Putin up on his offer of cooperation, but on US terms.

"I do think the United States and Russia can help each other, if not now, certainly in the aftermath of this thing," he said. "Whether and to what degree Americans are willing to offer some normalization in exchange for this is entirely up to us."