Frida Ghitis is a world affairs columnist for The Miami Herald and World Politics Review, and a former CNN producer and correspondent. The views expressed in this commentary are her own.

(CNN) After more than two hours of talks on Friday, Presidents Donald Trump and Vladimir Putin appeared to have made progress in bridging some of the issues dividing their countries. But it's far too soon to declare success in ending the hostility that has marked recent US-Russia relations.

President Trump exceeded expectations at the meeting, principally by bringing up the issue of Russia's interference in the US elections. Just 24 hours earlier, Trump mused that "Nobody really knows for sure" who was responsible for hacking the elections. The Russian foreign minister, Sergey Lavrov, reportedly told Russian media that Putin denied interfering and Trump accepted his denial. Secretary of State Rex Tillerson had a sharply different version of the conversation, saying the two countries could not come to an agreement on the issue.

The leaders reached agreement on other major matters, including a partial ceasefire in southwest Syria, which is a positive sign, but similar efforts have fizzled out in the past, so we should hope for the best but reserve judgment. They discussed Ukraine, the subject of sharpest disagreement, along with other key issues.

For Putin, the meeting was an even greater success. Above almost anything else, Putin wants to be seen as a major player on the global stage, and he achieved that in spades, beginning with the photo-op during which President Trump publicly declared it an "honor" to meet the Russian president (a man described by Defense Secretary James Mattis as a "threat to the global order," and whose interference in the US elections has been described by some members of Congress as an "act of war.")

But even before today's meeting, Putin had reason for satisfaction. While the United States has not lifted sanctions against Russia, one of the Russian President's top priorities, Putin can take great pleasure in watching what has happened to the West since Donald Trump became President.

The Western alliance is deeply divided -- and therefore weakened. The United States and its European friends no longer see eye-to-eye on key issues. The Trump administration has vowed to mostly set aside issues such as human rights and democracy promotion in foreign policy.

And, despite President Trump's belated support for NATO's mutual defense commitment, America's allies are less sure than ever before about the depth of Washington's commitment to the European Union and its efforts to strengthen democracy.

As with other campaign promises and foreign policy ideas, Donald Trump has discovered that improving relations with Russia is easier said than done -- so long as you also remain committed to safe-guarding US interests.

Perhaps some in his campaign rallies thought the notion of re-engaging with Russia was a novel concept. It isn't. Every US president since the end of the Cold War has tried it. And even during Soviet times, US leaders saw the benefit of working together in areas of common interest.

Franklin D. Roosevelt clenched his jaw and joined with Joseph Stalin to defeat Hitler. More recently, George W. Bush famously met with Vladimir Putin in 2001, "looked the man in the eye," and said he could "get a sense of his soul."

Later, when Putin sent Russian troops into the sovereign nation of Georgia , Bush had to re-evaluate what he had seen in Putin's soul.

The Obama administration also tried various approaches, all aimed at developing better relations. There was the infamous "reset" and Obama's just as-infamous hot-microphone whisper to then-Russian president Dmitry Medvedev that he would have "more flexibility" to work with Russia after the elections.

Ties unraveled further after Russia's heavy-handed interference in Ukraine, with the annexation of Crimea, and Russia's military intervention and support for Ukrainian separatists. That was the straw that brought down the pretense of rapprochement and triggered sanctions. The deterioration continued when Putin sent his forces to fight in Syria, on the side of President Bashar al-Assad and Iran.

JUST WATCHED Things Trump has said about Putin Replay More Videos ... MUST WATCH Things Trump has said about Putin 01:27

For Trump, improving relations with Russia is particularly difficult because of the dark cloud of election hacking and his continuing equivocation on the issue. Despite consensus among US intelligence agencies -- including Trump's own appointees -- that it was Russia that hacked the US election, Trump is still hedging.

Questions remain about why, exactly, Trump so consistently praises Putin and criticizes America's allies. Assuming that Trump's interest is nothing other than America's, there are very real reasons why Russia and the US so often disagree: The two countries have conflicting goals in many areas.

That became evident, early in Trump's term, when Russia's Syrian allies used chemical weapons against civilians, prompting Trump to launch missiles. The US and Russia agree on the need to defeat ISIS and return stability to Syria, but they profoundly disagree about what should come next, for reasons that go beyond Syria, including the influence of Iran and the Sunni-Shiite divide afflicting the Middle East.

US intelligence says Russia has only increased its spying activity in the United States and warns of a significant Russian threat to America's next election. For Putin, this is likely reason to grin. Even more satisfying must be the turmoil that has followed the US election, which makes democracy seem less appealing, potentially sapping some energy from demands for more democracy in Russia, where he has hollowed out of any semblance of democratic fair play.

Putin is an experienced, wily operator. Just hours before the Trump-Putin meeting, Russia blocked a US resolution on North Korea at the UN Security Council. It might have been a case of Putin flexing his muscle to show how much power he has to help or hurt the US.

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The first direct meeting between Donald Trump and Vladimir Putin surprised many with the amount of substance it contained. But while Trump is just getting to know the Russian President, the United States has many years of experience with Putin. Presidents looking after US interests have found that, while there is room for cooperation on specific issues, positive early meetings often lead to disappointment later. Friday was a great day for Putin, a good one for Trump. For the rest of the world, we'll have to wait and see what actually materializes after the talks.