Ukrainian President Volodymyr Zelenskyy is expected at the White House on Tuesday for talks with U.S. President Donald Trump, as he looks to shore up support for Kyiv at a time when the Russia and Iran conflicts have shown signs of converging.

The meeting comes as the U.S war against Iran and Russia's full-scale invasion of Ukraine reach critical junctures. Trump has paused airstrikes against Iran as part of a push to give diplomacy another chance, while Zelenskyy has been galvanized by a flurry of deep-strike successes on Russian territory.

There appears to be no immediate end in sight for either conflict, however. In fact, the sprawling Middle East war has threatened to overlap with the Russia-Ukraine conflict in recent days.

Kyiv on Saturday launched an attack on an Iranian commercial vessel in the Caspian Sea, an incident which Tehran said left one sailor dead and injured several others. The Islamic Republic has threatened retaliation over the strike, with Foreign Minister Abbas Araghchi saying via social media that it "CANNOT GO UNANSWERED."

In a post on X on Saturday, Zelenskyy said Ukraine had "achieved very strong results with long‑range strikes in the Caspian Sea – including vessels used in military cargo shipments involving Iran, as well as a warship."

Christopher Granville, managing director at TS Lombard, described Ukraine's attack on an Iranian vessel in the Caspian Sea as a "very significant" development.

"The Ukrainian President Volodymyr Zelenskyy has himself spoken of these strikes with satisfaction and justified them on the grounds that Ukrainian intelligence has evidence that Russian intelligence is helping Iran with targeting U.S. military sites in neighboring Middle Eastern countries," Granville told CNBC's "Europe Early Edition" on Monday.

"It's a collision of these wars. It's a merger. I think fundamentally this is very significant. Militarily how significant it is remains, of course, to be seen, but Iran has said in its public statement that it will hit back and that Ukraine has made a mistake which it will regret," he added.

Ukrainian authorities may be calculating that Iran has its hands full with its war with the U.S., Granville said, "but as it happens, the military exchanges between [the] U.S. and Iran have died down in the last two or three days. So, yeah, it's a big deal."

Ukraine's Foreign Minister Andrii Sybiha on Monday described Iran's threats of retaliation as "unjustified and groundless."

The regime in Tehran "is a direct accomplice to Russian aggression against Ukraine, fuelling Moscow's criminal war with weapons that have killed Ukrainians since 2022," Sybiha said via X, referring to the start of Russia's war against Ukraine.

Russia has long used Iranian-designed Shahed drones in its war on Ukraine, a weapon that analysts sometimes refer to as "the poor man's cruise missile."

Hamidreza Azizi, an expert on Iranian security and visiting fellow at Berlin-based think tank SWP, said that at the political level, Iran could respond to Ukraine's attack by recognizing Crimea and the Donbas as parts of Russian territory, areas occupied by Russia that Tehran has so far refused to endorse.

"In any case, what is clear is that Iran's war is becoming increasingly intertwined with two other conflicts: the Saudi-Houthi confrontation and the Russia-Ukraine war," Azizi said Sunday in a social media post.

"With each passing day, the war is evolving into an increasingly complex, multidimensional, and international conflict, he added.

Alongside Israeli Prime Minister Benjamin Netanyahu, Zelenskyy is expected to attend the Washington funeral of the late Sen. Lindsey Graham at a service on Tuesday. Both leaders are scheduled to meet with Trump during their visits.

For Zelenskyy, the meeting represents a chance to further improve his relationship with Trump, roughly 17 months on from an Oval Office meeting that unraveled into an extraordinary shouting match.

— CNBC's Azhar Sukri contributed to this report.