An explosion in Delhi injured one diplomat and three other people. Witnesses told local TV two people on motorcycles had placed a device on the car when it stopped in traffic.
A bomb underneath a diplomat's car in Tbilisi was found and defused.
Israeli leader Benjamin Netanyahu said Iran was behind the two incidents.
"Today we witnessed two attempts of terrorism against innocent civilians," he told a meeting of his Likud party MPs.
"Iran is behind these attacks and it is the largest terror exporter in the world."
He also blamed Iran for recent plots to attack Israeli targets in Thailand and Azerbaijan that were prevented.
And he suggested that the militant Islamist Hezbollah movement was also involved.
Israel's foreign ministry said that Israel had the ability to track down those who carried out the attacks.