Mossack Fonseca "will be ceasing operations" in those territories, "but we will continue serving all of our clients," it said.
"This decision has been taken with great regret, as Mossack Fonseca has had a presence in these locations for more than 20 years," the Panama-based law firm added.
The office closures were part of a strategy to "consolidate our service office network," it said.
The announcement came nearly eight weeks after the first reports about the Panama Papers emerged, divulging details taken from nearly four decades of records from Mossack Fonseca's computer archives.
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Although offshore companies are not in themselves illegal, the sudden publication of the information drew attention to possible tax avoidance and money laundering crimes in some cases, and embarrassed some figures trying to keep their finances secret.
News of the closure of Mossack Fonseca's offices in Jersey and Isle of Man -- two Crown dependencies of Britain -- and Gibraltar -- a British overseas territory jutting off from Spain -- was reported earlier this week by local media in those territories and the BBC.
While its tweets yesterday said those closures were happening, they made no mention of another report circulating this week in US media, about Mossack Fonseca's affiliate in the state of Nevada resigning as the agent for 1,000 companies it administered there.