This exchange marks the highest-profile disagreement between the President and Musk.
The central bank left its benchmark rate ILINR=ECI at 4.50%.
Major stock indexes plunged on Monday as Trump showed no sign of backing away from his tariff plans.
The Trump administration applied a 10% tariff to islands without a human population - was this an oversight or a security policy?
The meeting was "warm, friendly and productive," according to Israel's Government Press Office (GPO).
Trump's announcement of a 10% baseline tariff on all trade partners, plus additional duties for many countries, has sent global markets spiraling.
The two will discuss issues including the hostage crisis, finishing the war in Gaza, and tariffs that were recently imposed by the Trump administration on Israel.
What makes this decision particularly galling is the timing. On Tuesday, Israel officially removed all tariffs on American products.
Musk, a Trump adviser who has been working to eliminate wasteful US public spending, spoke via video-link at a congress in Florence of Italy's right-wing, co-ruling League Party.
This comes after Prime Minister Benjamin Netanyahu talked to Trump about the tariffs.
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