It was an awkward break in summit protocol, as President Vladimir V. Putin of Russia chatted for 45 minutes with his Indian counterpart inside a bulletproof Russian-made limousine that sat idling while other world leaders waited.

But for Mr. Putin, his presidential state car, which he took to China this week as he met with other leaders, was an ideal setting for personal diplomacy, one that his spokesman said offered a “home court advantage.”

In a three-day span, both Prime Minister Narendra Modi of India and North Korea’s leader, Kim Jong-un, hitched rides with Mr. Putin in his hulking black Aurus limousine.

For Mr. Modi, a short drive with Mr. Putin during a Eurasian summit meeting on Monday in Tianjin, China, led to their long back-seat conversation. Mr. Kim’s turn came on Wednesday, when he rode with the Russian president from a banquet in Beijing to a state guesthouse where they held bilateral talks affirming their countries’ growing ties.

Both drives were eagerly promoted by the Kremlin. The one with Mr. Modi, perhaps Mr. Putin’s highest-profile passenger yet, was portrayed as a spontaneous decision, though there was enough time to alert the cameras to what amounted to a demonstration of unity between two leaders pushed closer together by President Trump’s diplomatic swerves.